# Precalculus Concepts and Exam Problems

### Course Description

In this mini-lecture series, Robert Donley (MathDoctorBob) walks you through important advanced topics in PreCalculus through example problems, showing you both the theory behind the problems, and how to solve them. He shows you trigonometric identities and laws such as the Law of Sines and Law of Cosines, complex numbers including cube roots and De Moivre's theorem, arithmetic sequences and sums, geometric sum, proof by induction, the binomial theorem, composition of functions, projectile motion, factorization of polynomials, partial fraction, exponential and inverse functions, and much more.

Whether you are a high school student learning this material for the first time, or someone in need of a quick college algebra refresher, this short course will be invaluable to you.

Math Doctor Bob in Mini-Lecture 34: Example of Proof of Trig Identity
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### Video Lectures & Study Materials

# Lecture Play Lecture
1 Example of Arithmetic Sequence (2:07) Play Video
2 Example of Arithmetic Sum (5:24) Play Video
3 Geometric Proof of Integer Sum Formula (3:28) Play Video
4 Example of Geometric Sum (4:34) Play Video
5 Example of Proof By Induction (4:48) Play Video
6 Example of Proof by Induction 2: 3 divides 5^n - 2^n (9:15) Play Video
7 Example of Proof by Induction 3: n! less than n^n (6:14) Play Video
8 Example of Binomial Theorem (8:07) Play Video
9 Example of a Piecewise-Defined Function (6:40) Play Video
10 Domain of sqrt(x+1) - 1/sqrt(9-x^2) (5:00) Play Video
11 Example of Composition of Functions (5:55) Play Video
12 Graph of y = -2sqrt(x+4) - 3 (5:35) Play Video
13 Example of Projectile Motion (4:02) Play Video
14 Inverse Function for f(x) = (x-2)/(x+2) (12:06) Play Video
15 Using Synthetic Division to Evaluate a Polynomial (4:03) Play Video
16 Fast Factorization of Polynomial (7:22) Play Video
17 Multiplying Complex Numbers (4:57) Play Video
18 Complex Conjugate Roots of a Real Polynomial (4:54) Play Video
19 Factoring 3x^4-2x^3+3x-2 Over The Complex Numbers (5:45) Play Video
20 Sketch of Rational Function (7:10) Play Video
21 Partial Fraction Expansion of (x^4+x^3+1)/(x(x^2+1)^2) (4:20) Play Video
22 Evaluation of 3ln(2e^2) + 2ln(3/e) - ln(72e) (6:32) Play Video
23 Domain of ln((x+1)/(x-1)) +ln(x-1)-ln(x+1) (4:21) Play Video
24 Solving an Exponential Equation (3:55) Play Video
25 Memorizing Trig Values: Three Easy Pieces (13:03) Play Video
26 Trig Values for Multiples of pi/5 (6:58) Play Video
27 Examples of Values of Trig Functions (4:08) Play Video
28 Calculating Trig Values (6:18) Play Video
29 Examples of Inverse Trig Evaluations (8:33) Play Video
30 Graph of y = -4sin(3x-pi) (5:10) Play Video
31 Graph of y = 2 sec(pi x - pi/3) (5:34) Play Video
32 Example of Converting to Polar Coordinates (7:48) Play Video
33 Example of Graph of Polar Equation (4:37) Play Video
34 Example of Proof of Trig Identity (5:02) Play Video
35 Example of Double Angle Formulas (4:02) Play Video
36 Example of Half Angle Formula (4:47) Play Video
37 Example of Trig Equation (3:47) Play Video
38 Trig Values for Multiples of pi/5 (6:58) Play Video
39 Example of De Moivre's Theorem (3:43) Play Video
40 Cube Roots of -8 (10:01) Play Video
41 Complex Solutions of z^4-4z^2+16=0 (5:48) Play Video
42 Example of Law of Sines (7:13) Play Video
43 Example of Law of Cosines (10:37) Play Video