If #sin theta = sqrt5/3# then what is #cos 2 theta#?

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If #sin theta = sqrt5/3# then what is #cos 2 theta#?

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Answer 1 · 2016-06-11T09:22:22

#\cos(2\theta)=-1/9#. It does not depend on the quadrant #\theta# is in.

Explanation:

Double angle identities for cosine:

#cos(2\theta)#
#=2cos^2(\theta)-1#
#=cos^2(\theta)-sin^2(\theta)#
#=1-2sin^2(\theta)#

Note that there are only even powers of #sin(\theta)# and #cos(\theta)#. So any sign differences between quadrants cancels out, and if you know either #sin(\theta)# or #cos(\theta)# you have only one value for #cos(2\theta)#.

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If #sin theta = sqrt5/3# then what is #cos 2 theta#?

1 Answer

Explanation:

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