What is #cos^theta# in terms of #sintheta#?

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Answer 1 · 2015-12-18T00:14:58

If #theta# is in Q1 or Q4 then #cos theta = sqrt(1-sin^2 theta)#

If #theta# is in Q2 or Q3 then #cos theta = -sqrt(1-sin^2 theta)#

We always have #cos^2 theta + sin^2 theta = 1# regardless of which quadrant #theta# is in. Hence we always have:

#cos theta = +-sqrt(1-sin^2 theta)#

If #theta# is in Q1 or Q4 then #cos theta >= 0#, hence:

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

If #theta# is in Q2 or Q3 then #cos theta <= 0#, hence:

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