How do you determine $costheta$ given $sintheta=1/4,0<theta<pi/2$ ?

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Answer 1 · 2016-12-03T17:12:07

Use the identity $cos(theta) = +-sqrt(1 - sin^2(theta))$
Please see the explanation.

Use the identity $cos(theta) = +-sqrt(1 - sin^2(theta))$

Given that $0 < theta < pi/2$ then the cosine function is must be positive and the we must make the $+-$ be only positive:

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

Substitute $(1/4)^2$ for $sin^2(theta)$ :

$cos(theta) = sqrt(1 - (1/4)^2)$

$cos(theta) = sqrt(1 - 1/16)$

$cos(theta) = sqrt(15/16)$

$cos(theta) = sqrt(15)/4$

How do you determine costhetacostheta given sintheta=1/4,0<theta<pi/2sintheta=1/4,0<theta<pi/2?