How do you find the exact value of cos(theta) if sin(theta)=-2/3?

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polaris Share
Nov 8, 2015

Answer:

#cos theta = sqrt 5/3# (you didn't mention where your theta is)

Explanation:

#sin theta = y/h#
#cos theta =x/h#
but #x^2 +y^2 =h^2#
therefore #x^2 = h^2 - y^2 = 3^2 -(-2)^2 = 9- 4 =5#
#x = sqrt5#
thus, #cos theta = sqrt5/3#
since your #sin theta# is negative, theta could either be in Q III or Q IV
in Q III #cos theta = - sqrt5/3#, in Q IV # cos theta = + sqrt5/3#

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