sinθ=9/41 and cosϕ=−8/10, both angles terminate in Quadrant II find the exact value of cos(θ+ϕ)

Question

 and , both angles terminate in Quadrant II find the exact value of 

You do not need to simplify any radicals.

Answer 1

Since θ and φ (I use this notation for the second angle) are in quadrant 2, we know that the cos is negative and sine is positive.

We find cos(θ) from Pythagorean identity

sin(θ)² + cos(θ)² = 1

cos(θ) = -40/41.

The same, we find sin(φ), using the same identity for that angle, and knowing it is positive.

sin(φ) = 6/10.

We know both sin and cos for both angles. You can calculate cos(θ+φ) using the values found above.

cos(θ+φ) = cos(θ)cos(φ) - sin(θ)sin(θ)

cos(θ+φ) = .648780487...

Any questions?