Please Help! Pre-calculus and Trigonometry.

Question

sin a = - 4/5, quadrant III, cos B = - 15/17, quadrant III. Find sin (a-B).

Answer 1

in quadrant 3, sine and cosine are negative and tangent is positive;

sin A = -4/5 ---> adjacent = -3, opposite = -4, hypotenuse = 5

So then cos A = -3/5

cos B = -15/17 ---> adjacent = -15, opposite = -8, hypotenuse = 17

So then sin B = -8/17

sin(A-B) = sinA cosB - sin B cos A = (-4/5)(-15/17) - (-8/17)(-3/5)

= 60/85 - 24/85

= 36/85

Answer 2

There are two ways in which you can find the sines and cosines. Using a reference triangle, like Patrick did (from the comment above) or by using the Pythagorean identities, which is the approach I took. Either works just as well!