What is the value of $costheta$ if $sintheta=1/2$ and $theta$ is in $Q2$ ?

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Answer 1 · 2016-12-03T14:19:47

$costheta=-sqrt3/2$

As domain of $theta$ is $90^o< theta<180^o$ ,

while $sintheta$ is positive, $costheta$ is negative.

As $sintheta=1/2$ , and $sin^2theta+cos^2theta=1$

we have $cos^2theta=1-sin^2theta$ and as $costheta$ is negative

$costheta=-sqrt(1-sin^2theta)=-sqrt(1-(1/2)^2)$

= $-sqrt(1-1/4)=-sqrt(3/4)=-sqrt3/2$

What is the value of costhetacostheta if sintheta=1/2sintheta=1/2 and thetatheta is in Q2Q2?