If 180°<α<270°, cos⁡ α=−8/17, 270°<β<360°, and sin⁡ β=−4/5, what is cos⁡(α+β)?

Answer 1

In Q3, sin and cos are negative; in Q4, sin is negative and cos is positive.

Recall Pythagorean triples 3-4-5 and 8-15-17

Then, when cos ∝ = -8/17, sin ∝ = -15/17

When sin β = -4/5, cos β = 3/5

Then, cos(∝ + β) = cos ∝ cos β - sin ∝ sin β = -8/17*3/5 - -15/17 * -4/5 = -24/85 - 60/85 = -84/85