Question

If sin x = 3/5 and sin y = 5/13 , find the exact value of cos(x-y)

Answer 1

You'll need the identity for the cosine of a difference:

\(\Large \cos(x-y)=\cos(x)\cos(y)+\sin(x)\sin(y)\)

And you'll also need the fundamental ID:
\(\Large \sin^2\alpha + \cos^2 \alpha =1\)

...because you need to find the 2 missing cosine values.

However, in this kind of problem, you are usually also given the quadrant location of x and y... was that given? Because you'll need that in order to know the sign on the missing cosine values. The fundamental ID will only get it to within a \(\pm\), so knowing the quadrant lets you determine the correct sign.

Here, both of your sine values are positive, so x and y are each in either Q1 or Q2, but in one case that means positive cosine and in the other that means negative cosine, so I'm not sure how you can pin it down from the provided information.