Given $sintheta=-9/22$ and $270<theta<360$ , how do you find $sin2theta$ ?

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Answer 1 · 2016-07-08T12:49:00

$-9sqrt(403)/242$

you know that

$sin2theta=2sinthetacostheta$

since $sintheta=-9/22$

and you know that, in the fourth quadrant:

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

and, in this case,

$costheta=sqrt(1-(-9/22)^2)$

$=sqrt(1-81/484)$

$=sqrt(403)/22$

so

$sin2theta=2(-9/22)(sqrt(403)/22)$

$=-9sqrt(403)/242$

Given sintheta=-9/22sintheta=-9/22 and 270<theta<360270<theta<360, how do you find sin2thetasin2theta?