How do you determine $costheta$ given $sintheta=-1/5,pi<theta<(3pi)/2$ ?

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Answer 1 · 2017-09-11T10:37:50

$cos theta= -(2sqrt6)/5$

$theta$ is in 3rd quadrant where both $sin theta and cos theta$

is negative. $sin theta = 1/-5 :. sin^2 theta = 1/25$

$cos theta = +-sqrt(1-sin^2 theta) = +-sqrt (1-1/25) =+-sqrt 24/5$

Since $cos theta$ is negative in 3rd quadrant ,

$cos theta= -sqrt 24/5 or cos theta= -(2sqrt6)/5$ [Ans]

How do you determine costhetacostheta given sintheta=-1/5,pi<theta<(3pi)/2sintheta=-1/5,pi<theta<(3pi)/2?