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!