Section 8-5 Solving More Difficult Trigonometric Functions

To solve these functions, our goal is to isolate the function, much like we isolate the variable in Algebra. To do this, we will need to think about the operations that “undo” each other and the order in which we need to perform these steps.

Essentially, our final solution will be the angle(s) that make the equation true. We still need to remember where each function is positive and negative.

Example 1: Solve 2 sin 2 θ – 1 = 0, for 0º ≤ θ < 360º θ = 45º, 135º, 225º, 315º

Example 2: Solve 4 cos 2 θ – 3 = 0, for 0º ≤ θ < 360º θ = 30°, 150°, 210°, 330°

Example 3: Solve 3 csc 2 θ = 4, for 0º ≤ θ < 360º θ = 60º, 120º, 240º, 300º

HOMEWORK (Day 1) pg. 326; 1 – 4

If there is more than one trig. function, get everything on one side of the equation and then factor or get all of the functions in the same terms. Anytime that you have sine or cosine equal to 0, 1, or -1, you can use the unit circle to solve.

Example 4: Solve cos 2 x – 3 cos x = 4, for 0 ≤ θ < 2π x = π

Example 5: Solve 6 sin 2 x – 7 sin x = -2, for 0º ≤ θ < 360º x = 41.8º, 138.2º, 30º, 150º

Example 6: Solve cos x tan x = cos x, for 0º ≤ θ < 360º x = 45º, 90º, 225º, 270º

HOMEWORK (Day 2) pg. 326; 6, 10, 11