Solving Conditional Trigonometric Equations Section 4 2 Basic

4. 2 Basic Cosine Equations Summary: Solving cos x = a 1. If – 1 < a < 1 and a ≠ 0, then the solution set to cos x = a is {x|x = s + 2 kπ or x = 2π – s + 2 kπ}, where s = cos– 1 a and k is any integer. 2. The solution set to cos x = 1 is {x|x = 2 kπ}. 3. The solution set to cos x = 0 is {x|x = π/2 + kπ}. 4. The solution set to cos x = – 1 is {x|x = π + 2 kπ}. 5. If |a| > 1, then cos x = a has no solution. Copyright © 2011 Pearson Education, Inc. 3

4. 2 Basic Sine Equations Summary: Solving sin x = a 1. If – 1 < a < 1, a ≠ 0, and s = sin– 1 a, then the solution set to sin x = a is {x|x = s + 2 kπ or x = π – s + 2 kπ} for s > 0, and {x|x = s + 2π + 2 kπ or x = π – s + 2 kπ} for s < 0. 2. The solution set to sin x = 1 is {x|x = π/2 + 2 kπ}. 1. The solution set to sin x = 0 is {x|x = kπ}. 2. The solution set to sin x = – 1 is {x|x = 3π/2 + 2 kπ}. 3. If |a| > 1, then sin x = a has no solution. Copyright © 2011 Pearson Education, Inc. 4

4. 2 Basic Tangent Equations Summary: Solving tan x = a If a is any real number and s = tan– 1 a, then the solution set to tan x = a is {x|x = s + kπ} for s ≥ 0, {x|x = s + π + kπ} for s < 0. and Copyright © 2011 Pearson Education, Inc. 5