If Sinθ = 1/3, what is CosθSin2θ?

Question

Using Sin^2 + cos^2 = 1

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Answer 1 · 2018-05-03T00:24:41

$16/27$

To find $costheta$

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

$costheta= +-sqrt(1-(1/3)^2)$

$costheta= +-(2sqrt2)/3$

Depends on what quadrant this angle is in determines whether the cosine value is negative or positive.

Apply sine double angle identity:
$costheta*2sinthetacostheta$

$(+-(2sqrt2)/3)*2(1/3)(+-(2sqrt2)/3)=$

$16/27$