How do you find the value of costheta given sintheta=-3/5 and in quadrant IV?

1 Answer
Apr 23, 2018

costheta=4/5

Explanation:

In quadrant IV, sintheta is negative and costheta is positive. Keeping this in mind,

Recall the identity

sin^2theta+cos^2theta=1

We know sintheta=(-3/5), sin^2theta=(-3/5)^2=9/25

Then,

9/25+cos^2theta=25/25

cos^2theta=25/25-9/25

cos^2theta=16/25

costheta=+-sqrt(16/25)=+-4/5

As we noted earlier, cosine is positive in quadrant IV, so we want the positive answer:

costheta=4/5