161k views
2 votes
Cos A = 0.83 and cos B = 0.55. What is sin A + sin B?

1 Answer

6 votes
If you were looking for sin (A+B), this would be a more familiar problem.

There's an identity that'd apply here:

sin (A+B)=sin A cos B + cos A sin B = sin A (0.55) + (0.83) sin B. But we don't have the value of sin A or that of sin B.

So, I will make the assumption that angles A and B pertain to unit circles, that is, that the hypotenuse of these angles are both 1. In that case it takes just the application of the Pythagorean Theorem to find sin A and sin B.

If cos A = 0.83, then (cos A)^2 + (sin A)^2 = 1^2 = 1, so that
(sin A)^2 = 1 - (cos A)^2, or sin A = plus or minus sqrt(1 - (cos A)^2).

We'd find sin B in the same way. Then, we could write out sin A + sin B.

Forgive my asking, but I'd like for you to double-check to ensure that you have copied and shared all of the given problem. Is there any mention of "unit circle?"
User Colton Myers
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories