Find the exact value of sin(x-y) if tan(x) = -1/4, tan(y) = -1/5, x is in quadrant II, and y is in quadrant IV.

Answer 1

First you need to get the sin of x and the sin of y using the Theorem of Pythagoras.

Since tan(x) = -1/4, the sin of x in quadrant 2 is 1/sqrt(17).

Since tan y = -1/5, the sin of y in quadrant 4 is -1/sqrt(26)

Now use the addition formula for sin to get sin (x-y) and since you have been asked for "exact" values, you need to compute the value using fractions!