Question

If sin θ=16
and π2<​θ​<π
, find cos​θ​
.(1 point)
Responses

35√6
the fraction with numerator square root of 35 and denominator 6

−16
negative 1 sixth

−37√6
negative the fraction with numerator square root of 37 and denominator 6

−35√6

Answer 1

There's a typo: sin θ cannot equal 16. The intended value must be sin θ = √35/6. Using that and π/2 < θ < π (QII, where cosine is negative):

cos^2 θ = 1 − sin^2 θ = 1 − (35/36) = 1/36,
so cos θ = −√(1/36) = −1/6.