If sin θ=5/13 and cos x=4/5

Question

Find cos (θ+x)

So far, I came up with the answer:
(±48 - (±15)) / 65

And I know that the answer was marked out as wrong, did I go wrong with the signs? If so, what signs should I have used, is there a way of telling which quadrant is it in?

Thanks

Answer 1

Unless they say something, I'd assume QI. In that case,

sinθ=5/13 and cosθ=12/13
sinx=3/5 and cosx=4/5

cos (θ+x) = (12/13)(4/5)-(5/13)(3/5) = 33/65

Usually they specify a quadrant if they want to make you determine the sign of the quantities involved.