Given cos alpha = 8/17, alpha in quadrant iv, and sin beta = -24/25, beta in quadrant iii, find sin(alpha-beta)

Given , is in Quadrant IV,  , and is in Quadrant III, find

We can use the angle subtraction formula of sine to answer this question.



We already know that .

We can use the Pythagorean identity  to find .



Since is in Quadrant IV, and sine is represented as y value on the unit circle, we must assume the negative value .

As similar process is then done with  .



And since is in Quadrant III, and cosine in represented as x value on the unit cercle, we must assume the negative value .

Now we can fill in our angle subtraction formula!

What’s the question here? what have you been learning about?