If 180°<α<270°, cos⁡ α=−817, 270°<β<360°, and sin⁡ β=−45, what is cos⁡(α+β)?

Question

If 180°<α<270°, cos⁡ α=−817, 270°<β<360°, and sin⁡ β=−45, what is cos⁡(α+β)?

Answer 1

Alice, when you wrote cos a = -817, did you mean -8/17?

that will make a lot of sense. For example, the other leg of the triangle, by Pythagorean theorem, is exactly 15.

Also, when you wrote sin(b) = -45, did you mean “b = 45”, as John guessed?

Now, follow John’s procedure, recognizing that

since we know cos(a) = -8/17 in quadrant III, we know that sin(a)=-15/17.

if you have any questions, please ask.

Answer 2

If I put a decimal before -817; α=215.214......°

" " " " " -45: β=333.257.....°

cos(α+β)=cos=-.989090.....°

Answer 3

Angle A: COS^-1 (-.817) = 144.79° but in 3rd Quadrant = 234.79°

Angle B: -45° in 4th Quadrant is 315°

COS(A+B) = COS(A) x COS(B) - SIN(A) x SIN(B) = -0.9854