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#