SOLUTION: 36. sin(u-v) sin u=5/13 cosv=-3/5 find the exact value

Question 174442: 36. sin(u-v) sin u=5/13
cosv=-3/5
find the exact value
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
It is a little difficult to decipher what you are asking here. I think you mean find the exact value of given that and

First of all, you need the difference identity: .

Your problem is that you now need to determine given that and given that .

Knowing that , you are certain that is an angle in the First or Second Quadrants. Remembering that a 5-12-13 triangle is a right triangle and the fact that the sine function is defined as opposite/hypotenuse, we can see directly that (if is First Quadrant) or (if is Second Quadrant).

Similarly, must be Quadrant II or III because and 3-4-5 is a right triangle, so or

All you need to do is plug the values into or, in the case of this problem , and do the arithmetic. Because there are two possible values for each of the derived single angle functions, you will have 4 different calculations to perform, however you will end up with two pairs of identical results -- hence you will have two answers in the end.
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