# High School Mathematics: PreCalculus

## Video Lectures

Displaying all 145 video lectures.

Lecture 1Play Video |
Function vs RelationI introduce the concepts of Function and Domain. I compare and contrast them with coordinates, graphs, and equations through many examples. EXAMPLES at 5:14 11:02 16:05 18:12 21:33 23:05 |

Lecture 2Play Video |
Visually identifying key characteristics of graphsHow to identify key features of graphs such as relative maximum and minimum, zeros, domain, range, and y-intercept. We will also state the intervals where the graph is increasing, decreasing, and constant. |

Lecture 3Play Video |
Even Odd Polynomial Functions & SymmetryDefinining Even and Odd functions Newer video with many more examples at https://www.youtube.com/watch?v=WJvwUaRQdiY |

Lecture 4Play Video |
Even and Odd Functions Many ExamplesI explain how to determine if a function is even, odd, or neither and work through examples at Even Functions 3:39 5:03 8:33 10:42 11:23 Odd and Even Functions, or Neither 15:27 17:36 19:57 22:47 29:24 Please excuse the static from my mic. I have made adjustments to avoid this in the future. |

Lecture 5Play Video |
Piecewise FunctionsIntroduction to piecewise functions, graphing, domain, and range. |

Lecture 6Play Video |
Difference QuotientPreCalculus introduction to the Definition of the Difference Quotient |

Lecture 7Play Video |
Rate of Change Slope & Point Slope Equation of LinesIntroduction to finding slope and graphing lines. Please check out my other lessons about Linear Functions: Graphing Lines in Slope-Intercept form y=mx+b https://www.youtube.com/watch?v=xyVJZKu7Euw Graphing lines using X & Y Intercepts https://www.youtube.com/watch?v=KtgddI4qIok Equations of Lines and Graphing https://www.youtube.com/watch?v=Wmi1EysOHUQ Equations of parallel and perpendicular lines https://www.youtube.com/watch?v=ECljEiIgX_M Regression Lines and Correlation with TI-84 https://www.youtube.com/watch?v=L_h7nqNqgPs Linear Functions, their Attributes, & Interpreting Slope and y-Intercept https://www.youtube.com/watch?v=qbNTy0oMq1c Check out www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. |

Lecture 8Play Video |
Equations of Lines and GraphingContinued discussion about equations of lines and the three equation forms. Graphing of linear functions also included. Please check out my other lessons about Linear Functions: Graphing Lines in Slope-Intercept form y=mx+b https://www.youtube.com/watch?v=xyVJZKu7Euw Graphing lines using X & Y Intercepts https://www.youtube.com/watch?v=KtgddI4qIok Slope and Equations of Lines https://www.youtube.com/watch?v=xf8-BEdoSss Equations of parallel and perpendicular lines https://www.youtube.com/watch?v=ECljEiIgX_M Regression Lines and Correlation with TI-84 https://www.youtube.com/watch?v=L_h7nqNqgPs Linear Functions, their Attributes, & Interpreting Slope and y-Intercept https://www.youtube.com/watch?v=qbNTy0oMq1c Check out www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. |

Lecture 9Play Video |
Equations of Parallel and Perpendicular LinesAn introduction to finding the equations of lines that pass through a point and are parallel or perpendicular to a given line. Please check out my other lessons about Linear Functions: Graphing Lines in Slope-Intercept form y=mx+b https://www.youtube.com/watch?v=xyVJZKu7Euw Graphing lines using X & Y Intercepts https://www.youtube.com/watch?v=KtgddI4qIok Slope and Equations of Lines https://www.youtube.com/watch?v=xf8-BEdoSss Equations of Lines and Graphing https://www.youtube.com/watch?v=Wmi1EysOHUQ Regression Lines and Correlation with TI-84 https://www.youtube.com/watch?v=L_h7nqNqgPs Linear Functions, their Attributes, & Interpreting Slope and y-Intercept https://www.youtube.com/watch?v=qbNTy0oMq1c Check out www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. |

Lecture 10Play Video |
Average Rate of ChangeIntroduction to the average rate of change formula. |

Lecture 11Play Video |
Transformation of FunctionsI cover transformations of vertical and horizontal slides, vertical stretch, horizontal and vertical reflections to help you draw quick sketches of some common graphs. |

Lecture 12Play Video |
Composition of FunctionsI introduce composition of functions and discuss domain. |

Lecture 13Play Video |
Determining Domain of FunctionsI discuss finding domain of functions with the use of graphs or graphing calculators. The domain of the last example is no solution. Identifying Domain & Range from a Graph https://www.youtube.com/watch?v=1UAKQ_2yfxI&list=PLGbL7EvScm... |

Lecture 14Play Video |
Combining Functions & Function OperationsI go over combining functions through addition, subtraction, multiplication, and division. I also explain the restriction on domain of these combined functions |

Lecture 15Play Video |
Inverse FunctionsA graphic and algebraic approach to finding inverse functions. |

Lecture 16Play Video |
Modeling with Functions Part 1We model real life scenarios of sales and volume of a box with functions. These type of PreCalculus questions will help to prepare for the sections of Calculus called Related Rates. |

Lecture 17Play Video |
Modeling with Functions Part 2I continue with two more examples of Modeling with Functions which relate the area of regions with their perimeter. These type of questions will help to master the type of word problems you may see in the Related Rates sections of your Calculus book. |

Lecture 18Play Video |
Modeling with Functions Part 3I do two more examples: first involving relating surface area to the volume of a rectangular solid , and second looking at the volume of a cone in terms of it's radius and then it's hight. These type of PreCalculus questions will help to prepare for the sections of Calculus called Related Rates. |

Lecture 19Play Video |
Complex (imaginary) Numbers Part 1I introduce complex numbers, show how i-squared is -1, show how to graph them, and then go through a number of algebraic examples showing how to work with them. |

Lecture 20Play Video |
Complex (imaginary) Numbers Part 2I restart and finish the example from Complex Numbers Part 1. I solve a quadratic equation and find a solution that is a pair of complex numbers. I then graph the parabola to explain why we found the solution to be imaginary. |

Lecture 21Play Video |
Graphing Parabolas w/ vertex & interceptsI introduce the standard form of parabola and relate it to the transformations we just learned. I then graph a parabola in it's general form finding its vertex and X & Y intercepts. |

Lecture 22Play Video |
Parabola Applications Maximizing Minimizing Reflectors, etcI give examples of how parabolas apply to real life and work through two example...one about maximum height of a thrown object, and a second about maximizing area of a rectangle with a fixed perimeter |

Lecture 23Play Video |
Polynomial Graphs Part 1I introduce polynomial functions and give examples of what their graphs may look like. I then go over how to determine the End Behavior of these graphs. Part 2 will include finding y-intercepts, x-intercepts and their multiplicity, determining even or odd, and sketching the function. At minute 2:34 I say that f(x)=4 has an exponent of 0 instead of a degree of 0. At 7:04 I incorrectly draw y=-1/x instead of y=1/x...though my explaining about what a polynomial graph is still correct otherwise. An annotation was added but you won't see it with an iPad, iPod, or iPhone. |

Lecture 24Play Video |
Polynomial Graphs Part 2I continue my introduction of graphing polynomials without the assistance of a graphing calculator. I go over x-int & y-int, and I remind you how to determine if a function is even or odd to aid in graphing. |

Lecture 25Play Video |
Basic graphing with a TI-NSPIREI show how to graph a parabola, find it's vertex, and x-intercept on a TI-NSPIRE. |

Lecture 26Play Video |
Factoring OverviewI go over some common method of factoring binomials and trinomials. Here you can find a selection of my Factoring Lessons http://www.profrobbob.com/algebra-2/factoring-techniques |

Lecture 27Play Video |
Factoring by GroupingI work through 4 examples of factoring expressions and solving equations using factoring by grouping. Here you can find a selection of my Factoring Lessons http://www.profrobbob.com/algebra-2/factoring-techniques |

Lecture 28Play Video |
Solving Equations with 2 Absolute Value Functions or MoreI explain how to solve equations with two absolute value functions or more and then work through 3 examples at 3:48 14:13 22:57 In the last example after solving the equation I explain how to finish the problem if it were originally an inequality. |

Lecture 29Play Video |
Synthetic Division & Remainder TheoremI introduce Synthetic Division and the Remainder Theorem. Synthetic division is a short cut to long division when you are dividing by a binomial in the form of (x-c). The Remainder Theorm is how you can use Synthetic Division to aid in evaluating polynomials at particular x values. |

Lecture 30Play Video |
Long Division of PolynomialsI introduce long division and go over two examples. I also preview how long division will allow you to solve higher order equations. |

Lecture 31Play Video |
Solving Higher Order Polynomials Pt 1 Rational Zeros Descartes RuleIn a 2 part video I show you how to solve equations with a degree larger than 2 without the aid of a graphing calculator or computer. |

Lecture 32Play Video |
Solving Higher Order Polynomials Pt 2 Rational Zeros Descartes RuleIn a 2 part video I show you how to solve equations with a degree larger than 2 without the aid of a graphing calculator or computer. |

Lecture 33Play Video |
Finding polynomials using the Linear Factorization TheoremGiven the degree, the real and imaginary solutions, and a point the graph goes through, I use the Linear Factorization Theorem to find the original polynomial function. In the last problem, the question would have to specify that the coefficients of the polynomial are real. Otherwise complex solutions don't necessarily have to occur in conjugate pairs. |

Lecture 34Play Video |
Horizontal Asymptotes of rational equationsUsing limits, I explain how to find how to find horizontal asymptotes of rational equations. |

Lecture 35Play Video |
Graphing Rational Functions with Slant AsymptotesI show you how to find slant asymptotes of rational equations. |

Lecture 36Play Video |
Finding vertical asymptotes and holes of rational equationsFinding vertical asymptotes and holes of rational equations. |

Lecture 37Play Video |
Graphing Rational Functions Part 1I show how to graph a rational function with a vertical and horizontal asymptote, x-intercepts, y-intercepts, and even or odd symmetry. |

Lecture 38Play Video |
Graphing Rational Functions Part 2This rational function I graph has a horizontal asymptoto, a vertical asymptote, and a hole. |

Lecture 39Play Video |
Solving Polynomial InequalitiesI introduce solving polynomial inequalities. |

Lecture 40Play Video |
Solving Rational InequalitiesI introduce solving rational inequalities. After showing you the steps you should follow for these types of problems I work through two examples. In the second example I write less than 0 in the second through forth line of work. That should read less than or equal to, an annotation correction has been made but you will not see this without FLASH. |

Lecture 41Play Video |
Graphing Exponential Functions w/ t-table or TransformationsI explain how to graph exponential functions using tables and transformations from a parent function. Properties of these graphs are also discussed such as domain, range, asymptotes, etc. |

Lecture 42Play Video |
Logarithm IntroductionI introduce logarithms and show how to convert from logarithm form to exponential form. Yes, I know I mispelled logarithm on the chalk board. I blame it on the cold medicine I was taking! |

Lecture 43Play Video |
Change of Base Formula LogarithmsI start with examples of evaluating log expressions that don't require a calculator, then compare that with a problem that does require the change of base formula. |

Lecture 44Play Video |
Using Properties of Logarithms to Expand LogsI introduce the 3 properties of logarithms and use them in multiple examples about how to expand logarithmic expressions. Part 2 will include examples of condensing log expressions. There is an annotation correction at 9:43 but you will not see it without Flash. I should have wrote -3 instead of -5. |

Lecture 45Play Video |
Using Properties of Logarithms to Condense LogsIn this video I continue covering the uses of the properties of logarithms to condense logarithmic expressions. |

Lecture 46Play Video |
Graphing LogarithmsI introduce graphing Logarithms (which I know is mispelled!) and expain how they are an inverse of exponential functions. At 1:48 I misspoke and stated that all exponential growth functions pass through (1,0), but the point is actually (0,1) |

Lecture 47Play Video |
Solving Equations with Logarithms Pt 1PLEASE NOTE my final answer at 10:26 should be 3.968. There is an annotation correction but you can only see this if using FLASH. In a three part video I do many examples of solving equations using logarithms to move the variable out of the exponent. In part two we remove logarithms from the equation to solve for X. |

Lecture 48Play Video |
Solving Equations with Logarithms Pt 2In a three part video I do many examples of solving equations using logarithms to move the variable out of the exponent. In part two we remove logarithms from the equation to solve for X. |

Lecture 49Play Video |
Solving Equations with Logarithms Pt 3In a three part video I do many examples of solving equations using logarithms to move the variable out of the exponent. In part three I do examples with the log function on both sides of the equation. |

Lecture 50Play Video |
Solving Compound Interest ProblemsI go over examples involving compound growth and continuous compound growth. Some examples require the use of logarithms to solve for an unknown time period. I apologize that this video has some inconsistent rounding errors. The answer to the first equation without round off error is $40387.39 |

Lecture 51Play Video |
Standard Position Angles & Radians Part 1Part 1 of 2. I introduce Standard Position Angles, Define Coterminal Angles, Quadrantal Angles, and the Radian Measure. Standard Position Angles & Radians Part 2 https://www.youtube.com/watch?v=d0mmCN6rOXM&list=PL085526F86... |

Lecture 52Play Video |
Standard Position Angles & Radians Part 2In part 2 I show how to convert angles from degrees to radians and radians to degrees. I then introduce the sixteen angles around what will be developed into the unit circle. On the angle of 330 degrees, I said 330 but wrote 333. It is 330:D |

Lecture 53Play Video |
Setting up the Unit Circle Part 1 and Reference AngleIn a 2 part video I introduce the basic functions of Trigonometry (Sine, Cosine, and Tangent) and explain how to develop the unit circle using 45-45-90 triangle and 30-60-90 triangles you learned in Geometry. I also define reference angles. Setting Up the Unit Circle Part 2 https://www.youtube.com/watch?v=FaZ7frx8nd8&src_vid=j5SoWzBS... |

Lecture 54Play Video |
Setting Up the Unit Circle Part 2In a 2 part video I introduce the basic functions of Trigonometry ( Sine, Cosine, and Tangent ) and explain the design and use of the unit circle. I also review the definition of a reference angle. |

Lecture 55Play Video |
Linear & Angular Speed Part 1I go over examples of evaluating Linear Speed, Angular Speed, and finding Arc Length while measuring rotation using radians. In this video I keep saying Velocity matching language of textbooks I have used in the past, but since the measure of velocity also incorporates direction I should be saying speed. Linear & Angular Speed Part 2 https://www.youtube.com/watch?v=iMgckNT8K6s |

Lecture 56Play Video |
Linear & Angular Speed Part 2I go over examples of evaluating Linear Speed, Angular Speed, and finding Arc Length while measuring rotation using radians. In this video I keep saying Velocity matching language of textbooks I have used in the past, but since the measure of velocity also incorporates direction I should be saying speed. |

Lecture 57Play Video |
Evaluating Trig Functions w/ Unit Circle Degrees & RadiansI go over many example of evaluating trigonometry functions in exact form using the unit circle. |

Lecture 58Play Video |
Fundamental Trigonometric Identities Intro & ProofsI introduce and prove the Fundamental Trigonomic Identities...the Quotient Identities, Reciprocal Identities, and the Pythagorian Identities. |

Lecture 59Play Video |
Trig Expressions & Finding Trig Functions Given another Trig RatioI do a couple more examples of evaluating trig expressions using the unit circle. I then show you how to set up multiple Trigonometric Functions from a single angle....Say given Sine find Tangent of the same angle. |

Lecture 60Play Video |
Right Triangle Trigonometry Part 1: Finding Missing SidesI introduce evaluating trigonometric functions about a right triangle. We will set up the trig ratios given a right triangle, and find missing angle measures, and sides of right triangles using the pythagorean theorm and the trig functions. |

Lecture 61Play Video |
Right Triangle Trigonometry Part 2: Solving for Acute AnglesLink to Part 1 https://www.youtube.com/watch?v=pkjuVZUdcvo I introduce evaluating trigonometric functions about a right triangle. We will set up the trig ratios given a right triangle, and find missing angle measures, and sides of right triangles using the pythagorean theorm and the trig functions. |

Lecture 62Play Video |
Trigonometric CofunctionsI introduce the concept of Cofunctions in Trigonometry and explain why and when they are equal. |

Lecture 63Play Video |
Trigonometric Functions of Any AngleI introduce how to evaluate trig functions without knowing the actual angle measures. With just enough information to determine what quadrant an angle is in and set up the reference triangle, we can find any trigonometric ratio. |

Lecture 64Play Video |
Understanding Basic Sine & Cosine GraphsI use the unit circle to graph 2 periods the basic sine and cosine functions to show how they relate to each other. I also explain how the symmetry of these two graphs helps you to determine that the sine function is odd and the cosine function is even. |

Lecture 65Play Video |
Graphing Sine & Cosine w/out a Calculator Pt1I introduce the transformations you can apply to the six trigonomtric functions. I then go over two basic examples of graphing sine with using t-tables. Part 2 will be two more examples of graphing sine & cosine with more transformations using a t-table. Part 2 http://www.youtube.com/watch?v=c1VD_LEs5ZY&feature=share&lis... |

Lecture 66Play Video |
Graphing Sine & Cosine w/out a Calculator Pt 2I introduce the transformations you can apply to the six trigonomtric functions. I then go over two basic examples of graphing sine with using t-tables. Part 2 will be two more examples of graphing sine & cosine with more transformations using a t-table. |

Lecture 67Play Video |
Equation of Sine and Cosine from a Graph |

Lecture 68Play Video |
Water Depth Word Problem Modeled with Cosine Sine FunctionAnalyzing the time between high tides and the depth of the water, I make a function that models the tides and then calculate the safe hours for a ship to enter the port. At minute 13:27 I wrote the inverse cosine of .667 or arccos(.667), that should be arccos(-.667). |

Lecture 69Play Video |
Intro Tangent & Cotangent GraphsUsing the unit circle I explain why Tangent and Cotangent have a period of Pi instead of 2Pi like the other trig functions. I then graph the two parent functions discussing domain and range as well. |

Lecture 70Play Video |
Tangent & Cotangent Graphs w/ TransformationsI do two examples of Tangent and Cotangent that include multiple transformations with a t-table. This video has two errors noted below which have annotation corrections in the video which you will see if you have Flash. At minute 7:27 I say that the cot(0) is -1/0, that should be 1/0. The very last point I mention at around 10:42 should have a y coordinate of -1 not 0. Sorry for the small errors:) |

Lecture 71Play Video |
Graphing Secant & Cosecant w/ t-tableI show the reciprocal relationship between the Cosine and Secant graph and Sine Cosecant graph. This video includes two examples of graphing these inverse functions. Note the reciprocal identities CSC(theta)=1/SIN(theta) and SEC(theta)=1/COS(theta) as I work through these examples. |

Lecture 72Play Video |
Evaluating Inverse Trigonometric FunctionsI introduce Inverse Trigonometric Functions. I explain where the restricted range values of inverse sine, inverse cosine, and inverse tangent come from...and do a number of examples. |

Lecture 73Play Video |
Evaluating Inverse Trigonometric Functions (Full Length PLEASE READ DESCRIPTIONI introduce Inverse Trigonometric Functions. I explain where the restricted range values of inverse sine, inverse cosine, and inverse tangent come from...and do a number of examples. THIS VIDEO CONTAINS AN ANNOTATION CORRECTION FOR THE RANGE OF INVERSE TANGENT. Inverse Tangent has a range between -pi/2 & pi/2 but does not include these values. This should read -pi/2 is less than theta less than pi/2. I apologize for my error when copying my notes for the board. Evaluating Inverse Trigonometric Functions Corrected https://www.youtube.com/watch?v=7t_pZGGxMdE&list=PL085526F86... |

Lecture 74Play Video |
Verifying Trigonometric Identities - Part 1Using the fundemental identities and the Pythagorean Identities, I go over multiple examples of verifying trigonometric identities. It is very important in proofs that you do not handle it like an equation moving terms and factors from side to side. I was corrected that what I am trying to prove should not be within the body of the proof. This implies it has already been assumed to be true. So proofs should be shown like this example: cos^2(x)(tan^2(x)+1)=1 Proof: cos^2(x)(tan^2(x)+1)=cos^2(x)*sec^2(x) =cos^2(x)(1/cos^2(x)) =1 Verifying Trigonometric Identities Part 2 https://www.youtube.com/watch?v=q8k-sS7qRts Verifying Trigonometric Identities Part 3 https://www.youtube.com/watch?v=mAnw4ImaPK0 |

Lecture 75Play Video |
Verifying Trigonometric Identities - Part 2Using the fundemental identities and the Pythagorean Identities, I go over multiple examples of verifying trigonometric identities. It is very important in proofs that you do not handle it like an equation moving terms and factors from side to side. I was corrected that what I am trying to prove should not be within the body of the proof. This implies it has already been assumed to be true. So proofs should be shown like this example: cos^2(x)(tan^2(x)+1)=1 Proof: cos^2(x)(tan^2(x)+1)=cos^2(x)*sec^2(x) =cos^2(x)(1/cos^2(x)) =1 |

Lecture 76Play Video |
Verifying Trigonometric Identities Pt3Using the fundemental identities and the Pythagorean Identities, I go over multiple examples of verifying trigonometric identities. It is very important in proofs that you do not handle it like an equation moving terms and factors from side to side. I was corrected that what I am trying to prove should not be within the body of the proof. This implies it has already been assumed to be true. So proofs should be shown like this example: cos^2(x)(tan^2(x)+1)=1 Proof: cos^2(x)(tan^2(x)+1)=cos^2(x)*sec^2(x) =cos^2(x)(1/cos^2(x)) =1 |

Lecture 77Play Video |
Sum and Difference Trigonometric IdentitiesUsing the Sum and Difference Identities, I do examples of evaluating trigonometric expressions that require the use of the sum and difference identities for sine, cosine, and tangent. At the end of the example of sin(195) I say the denominator of the answer is 2 but 2*2 equals 4. Sorry for the error. There is an annotation correction, but you will not see it if you do not have Flash. |

Lecture 78Play Video |
Verifying Trigonometric Identities Involving Sum & DifferenceI work through some examples of verifying trig identities that require the use of sum & difference identities of Sine, Cosine, and Tangent I was corrected that what I am trying to prove should not be within the body of the proof. This implies it has already been assumed to be true. So proofs should be shown like this example: cos^2(x)(tan^2(x)+1)=1 Proof: cos^2(x)(tan^2(x)+1)=cos^2(x)*sec^2(x) =cos^2(x)(1/cos^2(x)) =1 |

Lecture 79Play Video |
Evaluating Trigonometry Expressions with Half and Double Angles Pt1In a 2 part video I work many examples of evaluating trigonometric expressions involving half and double angle identities. |

Lecture 80Play Video |
Evaluating Trigonometry Expressions with Half and Double Angles Pt2In a 2 part video I work many examples of evaluating trigonometric expressions involving half and double angle identities. |

Lecture 81Play Video |
Trigonometry Proofs Involving Half and Double AnglesI work through 5 examples of verifying trigonometric identities that involve half angle and double angle identities. I was corrected that what I am trying to prove should not be within the body of the proof. This implies it has already been assumed to be true. So proofs should be shown like this example: cos^2(x)(tan^2(x)+1)=1 Proof: cos^2(x)(tan^2(x)+1)=cos^2(x)*sec^2(x) =cos^2(x)(1/cos^2(x)) =1 |

Lecture 82Play Video |
Trigonometric Equations Single Angle 0 to 2pi RestrictionI do multiple examples of solving equations with trigonometric functions in them. This videos only includes trig functions with single angles such as sinx as opposed to sin(4x). |

Lecture 83Play Video |
Single Angle Trigonometric Equations All SolutionsI do multiple examples of solving equations with trigonometric functions in them. This videos only includes trig functions with single angles such as sinx as opposed to sin(4x). |

Lecture 84Play Video |
Trigonometric Equations Multiple Angles 0 to 2pi RestrictionI continue my examples of solving algebraic equations that involve multiple angles. |

Lecture 85Play Video |
Trigonometric Equations Multiple Angles All SolutionsI continue my examples of solving algebraic equations that involve multiple angles such as sin(2x). |

Lecture 86Play Video |
Oblique Triangles Law of SinesI introduce the Law of Sine and go over a couple of examples where there is one unique triangle. I finish with an example of finding area of an oblique triangle. |

Lecture 87Play Video |
Ambiguous Case for Law of SinesI introduce solving oblique triangles when the information given is in the SSA form...or the ambiguous case. In this setting there may be one solution, two solutions, or none at all. NOTE: At minute 14:37 I incorrectly stated 61*sin(39)=37.8, it is 38.4. At minute 16:50 I state that angle B is 48.4 degrees. I hit the wrong button, it is 50.2 degrees. There are annotation corrections, though they will not be visible on an iPhone or iPad. I am very sorry for the errors. |

Lecture 88Play Video |
Law of CosinesI introduce and do examples of solving oblique triangles using the law of cosine. |

Lecture 89Play Video |
Area of oblique triangles SAS SSS Heron's FormulaI introduce and do examples of finding the area of oblique triangles using two sides and an includeds angle, as well as using Heron's formula when you know all three sides. |

Lecture 90Play Video |
Applications of Law of Sines and CosinesI do four examples to help you understand how to solve some of your word problems that require Law of Sine and/or Cosine. |

Lecture 91Play Video |
Trigonometry Bearing Problems 4 ExamplesIn this lesson I start out explaining how Bearing describes a direction of movement. I then work through 4 examples. Example 1 involves Right Triangle Trigonometry SOHCATTOA at 4:24 Example 2 involves Pythagorean Theorem at 12:52 Example 3 involves Law of Cosine at 19:38 Example 4 we find a new Bearing using Law of Sine at 25:36 Right Triangle Trigonometry Part 1 https://www.youtube.com/watch?v=pkjuVZUdcvo&index=11&list=PL... Oblique Triangles Law of Sines https://www.youtube.com/watch?v=FtYbQ8X7U_w&list=PL085526F86... Law of Cosines https://www.youtube.com/watch?v=07w-wk8kRRE&index=39&list=PL... |

Lecture 92Play Video |
Understanding Polar CoordinatesI introduce Polar Coordinate System. |

Lecture 93Play Video |
Graphing Polar Equations, Test for Symmetry & 4 Examples CorrectedThis lesson first starts with how to test for symmetry in a polar graph. Symmetry to the Polar Axis at 1:34 Symmetry to the line Theta=pi/2 at 8:13 Symmetry to the Pole at 10:38 Special Types of Graphs Circles at 13:13 Limacons at 16:16 I explain how to recognize the 4 subcategories of Limacons which are Inner Loop, Cartiod, Dimpled, and Convex. EXAMPLE of graphing a Limacon with an inner loop at 20:29 Rose Curve introduced at 34:10 EXAMPLE with even number of petals at 38:01 EXAMPLE with odd number of petals at 49:36 Lemniscates introduced at 54:03 LAST EXAMPLE at 55:14 Graphing Calculator Example at 26:50 My introductory video of Understanding Polar Coordinates https://www.youtube.com/watch?v=tKi05dfUhAA |

Lecture 94Play Video |
Converting Coordinates between Polar and Rectangular FormI do two examples converting a point from rectangular to polar...then back to rectangular form. |

Lecture 95Play Video |
Converting Equations Between Polar & Rectangular FormI work through 8 examples of converting equations between rectangular and polar form. Graphing Ellipses and Circles https://www.youtube.com/watch?v=Ux8gEMccP9w |

Lecture 96Play Video |
Complex Numbers in Polar FormI explain the relationhip between complex numbers in rectangular form and polar form. I also do an example of converting back and forth between the two forms. |

Lecture 97Play Video |
Product & Quotient of Polar Complex NumbersI work through a couple of examples of multiplying and dividing complex numbers in polar form |

Lecture 98Play Video |
De Moivre's Theorem powers of Polar Complex NumbersI explain how to raise complex numbers in polar form by very high powers by using De Moivre's Theorem. The first example starts at 6:13 |

Lecture 99Play Video |
De Moivre's Theorem Roots of Polar Complex NumbersI do three examples of finding roots of complex numbers in polar form using De Moivre's Root Theorem. |

Lecture 100Play Video |
Introduction to VectorsIn this admittedly long winded video I introduce the basic vocabulary and concepts of vectors. Included definition/concepts are magnitude, direction, horizonal and vertical components, equal & opposite vectors, zero vector, unit vector, scaler multiple. I include examples of adding & subtracting vectors both graphically and numerically, applying a scaler multiple, and coverting vectors writing in terms of their horizontal & verical components into direction and magnitude. |

Lecture 101Play Video |
Writing Vector in terms of Magnitude & Direction ExampleI work through two examples of converting the description of a vector between Magnitude & Direction vs Horizontal & Vertical components. |

Lecture 102Play Video |
Vector Application ExamplesI work through 5 examples of application of vectors. NOTE: In the last example I state the wind speed is 27 mph, but then use a wind speed of 10 mph in my problem. I added annotations over the written example but you will not see this on your iPad or iPhone. The angle Theta in the work formula of the first example is "The difference between the angle the force is being applied and the direction of the work." Because I am just a math teacher and not a science teacher, I learned something from a viewer/teacher I am guessing. Here is there reply... 59ejf I liked your video. However, a couple of comments are warranted. First: Force and energy are not the same thing and should not be used interchangeably. In fact, the vertical component of the force exerted on the handle of your wagon imparts no energy on the wagon. In fact, it doesn't even do any work on the wagon. Thus there is NO waste of energy. Second: This gets complicated. For instance, if a person is holding a couple of five pound buckets away from her body, she will soon tire and have to quit holding them up. She is not doing any work on the buckets by holding them up, as work is force times distance. If the buckets don't move, no distance is travelled by the forces and no work is done. She is exerting a force, but the forces are static. Energy and work have the same units. If no work is done, no energy is expended. Yet if you ask her if she did any work, she will say duh, to exhaustion. Be careful with using humans in your physics problems. |

Lecture 103Play Video |
Dot Product & Angle Between VectorsI explain how to find the Dot Product and the properties of the dot product. I continue by explaining how to calculate the angle between to vectors, including the special cases of Parallel Vectors and Orthogonal Vectors. |

Lecture 104Play Video |
Projection of a Vector onto another VectorI work through projecting a vector onto another vector in two setting: 1) When the vectors are described with magnitude and direction. 2) When the vectors are described by their horizontal and vertical components. NOTE: If you check to see if the composite vectors (at the end of this video) are perpendicular, the dot product will not equal zero. I rounded off my work too much when working through the scaler multiple portion of the projection formula. |

Lecture 105Play Video |
Solving Linear Systems with Substitution and Linear CombinationI take a system of linear equations and show you how to solve it with substition and then with linear combination. I show how you could find one answer, no answer, or many answers. |

Lecture 106Play Video |
Solving 3 Variable Linear Systems Substitution / Gaussian EliminationI introduce how to solve 3 variable linear systems with the elimination method and then work through 2 examples that each have one unique solution. |

Lecture 107Play Video |
Applications of 3 Variable SystemsI work through 2 examples of solving 3 variable linear systems using the elimination method. I show how to find the equation of a parabola when you are given 3 random points the graph goes through in my first example. In the second example I figure out how some money was split between three investments. |

Lecture 108Play Video |
Non-Square 3 Variable Linear SystemsI work through 2 example of "solving" non square systems. When you have three unknowns and only 2 equations you will not be able to find numerical solutions, but we can learn how the three unknowns are related to each other. |

Lecture 109Play Video |
Partial Fraction Decomposition Part 1In a 2 part video I explain Partial Fraction Decomposition. This is the process where we can undo the addition of two algebraic fractions. Part one deals with linear factors in the denominator and part two deals with quadratic factors in the denominator. Partial Fractions Decomposition Part 2 https://www.youtube.com/watch?v=3qo527nyiaY |

Lecture 110Play Video |
Partial Fractions Decomposition Part 2In a 2 part video I explain Partial Fraction Decomposition. This is the process where we can undo the addition of two algebraic fractions. Part one deals with linear factors in the denominator and part two deals with quadratic factors in the denominator. |

Lecture 111Play Video |
2 Variable Non Linear Systems Substitution MethodI explain and work through 2 examples of solving 2 Variable Non Linear Systems with the Substitution Method. |

Lecture 112Play Video |
2 Variable Non Linear Systems Addition/Elimination MethodI explain and work through 2 examples of solving 2 Variable Non Linear Systems with the Addition Method. |

Lecture 113Play Video |
Graphing Linear InequalitiesI introduce how to graph 2 variable linear inequalities and work through 3 examples. |

Lecture 114Play Video |
Graphing 1 Variable InequalitiesI introduce graphing of vertical and horizontal lines and inequalities. |

Lecture 115Play Video |
Graphing Non-Linear InequalitiesI introduce how to graph non-linear inequalities and then finish by working through three examples. |

Lecture 116Play Video |
Graphing System of Linear InequalitiesI work through two examples of graphing systems of inequalities. The first example involve linear inequalities and the second example has non-linear inequalities. |

Lecture 117Play Video |
Graphing Ellipses & CirclesI introduce the 4 conic sections, explain the basic structure of Ellipses & Circles, and finish by working through three graphing examples after putting these equations in standard form. |

Lecture 118Play Video |
Graphing Hyperbolas in Standard FormI introduce the basic structure of hyperbolas discussing how to locate the vertices, foci, transverse axis, conjugate axis, asymptotes, etc. I finish by working through multiple examples. |

Lecture 119Play Video |
Graphing Parabolas in Standard FormI introduce the basic structure of Parabolas. After the introductory notes, I work through three examples from easy to the hardest example last. These examples are put into Standard Form before graphing by completing the square when needed. |

Lecture 120Play Video |
Application of EllipsesI work through three example of Applications of Ellipses. |

Lecture 121Play Video |
Application of HyperbolasI work through 2 examples of Application of Hyperbolas |

Lecture 122Play Video |
Applications of Parabolas in Standard FormI work through 2 examples of word problems involving parabolas. |

Lecture 123Play Video |
Rotated Conic Section Identifying & Graphing 4 ExamplesTwo examples of Identifying Rotated Conics at 5:53 Graphing a Conic Rotated 30 degrees at 15:19 Graphing a Rotated Conic with your Graphing calculator at 28:55 Graphing a Conic with a non unit circle angle of rotation and center not on the origin at 36:27 |

Lecture 124Play Video |
Introduction to Parametric EquationsI introduce the basic concepts of Parametric Equations. I then work through many examples of graphing with t-tables. |

Lecture 125Play Video |
Parametric Equations Eliminating Parameter TI do multiple examples of converting parametric equations into rectangular form by eliminating the parameter T. |

Lecture 126Play Video |
Intro to SequencesI introduce the concept and notation for sequences and finish with a couple of graphing examples. I then explain recursive formulas and do another 2 examples showing you how they work. For all my lessons on Sequences and Series go here:) http://www.profrobbob.com/pre-calculus/intro-to-sequences-ar... |

Lecture 127Play Video |
Summation Notation (Sigma)I introduce the Summation Notation...Sigma...and work through five examples related to the topic of sequences. For all my lessons on Sequences and Series go here:) http://www.profrobbob.com/pre-calculus/intro-to-sequences-ar... |

Lecture 128Play Video |
Factorial NotationI introduce the Factorial Notation or symbol. I then work through a number of examples of how to evaluate factorials, and examples of factorials in sequence notation and summation notation. For all my lessons on Sequences and Series go here:) http://www.profrobbob.com/pre-calculus/intro-to-sequences-ar... |

Lecture 129Play Video |
Arithmetic Sequence IntroductionI introduce the concept of Arithmetic Sequences and work through some examples. For all my lessons so far on Sequences and Series go here:) http://www.profrobbob.com/pre-calculus/intro-to-sequences-ar... |

Lecture 130Play Video |
Partial Sum Arithmetic SequenceI introduce the formula for finding the sum of 'n' terms of an arithmetic sequence. I then work through several examples. For all my lessons on Sequences and Series go here:) http://www.profrobbob.com/pre-calculus/intro-to-sequences-ar... |

Lecture 131Play Video |
Intro to Geometric SequencesI introduce the concept of Geometric Sequences and writing the general formula for this type of sequence. I finish by working through several examples. For all my lessons on Sequences and Series go here:) http://www.profrobbob.com/pre-calculus/intro-to-sequences-ar... |

Lecture 132Play Video |
Geometric Means in a Geometric SequenceI explain how to find missing Geometric Means within a Geometric Sequence. I finish with two examples...first one relatively easy...the second is not so much:) For all my lessons on Sequences and Series go here:) http://www.profrobbob.com/pre-calculus/intro-to-sequences-ar... |

Lecture 133Play Video |
Partial Sum Geometric SequencesI introduce the formula for finding the sum of 'n' terms of an geometric sequence. I then work through several examples. For all my lessons on Sequences and Series go here:) http://www.profrobbob.com/pre-calculus/intro-to-sequences-ar... |

Lecture 134Play Video |
Infinite Sum Geometric SeriesI introduce the formula for finding the Infinite Sum of a Geometric Series, explain briefly how it works, and I then work through multiple examples. For all my lessons on Sequences and Series go here:) http://www.profrobbob.com/pre-calculus/intro-to-sequences-ar... |

Lecture 135Play Video |
Converting Repeating Decimal to a FractionI explain how finding the sum of an infinite geometric series allows you to convert a repeating decimal into a fraction. For all my lessons on Sequences and Series go here:) http://www.profrobbob.com/pre-calculus/intro-to-sequences-ar... |

Lecture 136Play Video |
Induction ProofsI introduce the steps to doing an Induction Proof. I then work through three examples that I hope will help you understand the concept and complete your homework:) |

Lecture 137Play Video |
Binomial Theorem Introduction to Raise Binomials to High PowersI explain how Pascal's Triangle and the Binomial Theorem help you to quickly expand binomials raised to relatively high powers. My last example is using the Binomial Theorem to find a specific term within an expansion. |

Lecture 138Play Video |
Why Limits are Important in CalculusI give an overview of how limits are used in two main concepts of Calculus. Finding slope of a curve at a given point and finding area under a curve. |

Lecture 139Play Video |
Finding Real limits Graphical & Numerical ApproachI work through five examples of finding REAL limits by analyzing graphs and numerical tables. Infinite limits are not discussed in this video. EXAMPLES AT 2:51 5:17 8:45 12:00 14:03 Please Like, and Follow as well at: Facebook.com/profrobbob Twitter.com/profrobbob |

Lecture 140Play Video |
Properties of LimitsI introduce the properties of limits that allow you to find the real limit of a function as x approaches "a" without needing to make a t-table or graph the function. Please Like, and Follow as well at: Facebook.com/profrobbob Twitter.com/profrobbob |

Lecture 141Play Video |
Finding Limits with Properties Examples inc QuotientsI work through 6 examples of finding the limit of a function as "x" approaches "a"...though at the start I state that I am doing 4:\ Four of these examples involve quotients where the function may be undefined at "a". EXAMPLES AT 2:23 3:20 6:05 8:23 13:40 18:59 Please Like, and Follow as well at: Facebook.com/profrobbob Twitter.com/profrobbob |

Lecture 142Play Video |
Limits & ContinuityI explain how to test for Continuity at a given point and find Discontinuities in functions. I finish by working through a couple of examples. EXAMPLES 4:57 10:57. Though I say smooth and continuous a few times in this video, a function does not have to be smooth to be continuous. |

Lecture 143Play Video |
Limits of Piecewise FunctionI work through four examples of finding limits of piecewise functions using the properties of limits. EXAMPLES 0:20 5:57 10:50 15:10 Please Like, and Follow as well at: Facebook.com/profrobbob Twitter.com/profrobbob |

Lecture 144Play Video |
Slope of Tangent Line Derivative at a PointI explain how to find the instantaneous slope at a given point along a curve. I finish by finding the tangent line to that curve at that point. All three of the examples I work in this video have real values of slope and thus have a real limit as h approaches 0. I do examples that have vertical tangent lines at the point of tangency and thus an undefined slope in a later video. EXAMPLES at 8:39 13:11 20:21 Link to Full Length Introduction to Definition of Derivative and Tangent Line Problems. http://www.youtube.com/watch?v=eWxo7O506G8&feature=share&lis... |

Lecture 145Play Video |
Finding Derivative with Definition of DerivativeI work through two examples of finding the derivative of a function using the Definition of Derivatives. |