How do you find the value of cosθ given sinθ=35 and in quadrant IV?

1 Answer
Apr 23, 2018

cosθ=45

Explanation:

In quadrant IV, sinθ is negative and cosθ is positive. Keeping this in mind,

Recall the identity

sin2θ+cos2θ=1

We know sinθ=(35),sin2θ=(35)2=925

Then,

925+cos2θ=2525

cos2θ=2525925

cos2θ=1625

cosθ=±1625=±45

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

cosθ=45