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

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Answer 1 · 2018-04-23T04:32:02

#costheta=4/5#

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#