Trigonometry

Solutions

Problem Set #5

Use trig identities to simplify each expression as much as possible

1. sin⁴θ – cos⁴ θ sin²θ – cos² θ

2. 1 – cos² θ sin²θ

3. cos⁸ θ - sin⁸ θ (cos⁴ θ + sin⁴ θ)(cos² θ – sin² θ)

4. cos² θ - cos⁴ θ cos² θ sin² θ

Solve the following equation for x

2sin²x – cosx – 1 = 0

2(1-cos²x) – cosx -1 = 0 (trig identity)

-2cos²x - cosx + 2 – 1=0

2cos²x + cosx - 1 = 0

(2cosx -1) (cosx + 1) = 0

this happens if cosx = ½ or cosx = -1 which in turn happens if x = 60° or x = 180°

(but there are lots of other solutions as well since cosine is periodic)