How do you find the exact values of #costheta# and #tantheta# when #sintheta=-1/2#?

1 Answer
Dean R.
May 10, 2018

#cos theta = pm sqrt{3}/2 #

#tan theta = pm 1/sqrt{3}#

Explanation:

Get a new triangle, question writer! Seriously, there's nothing about this question that requires using one of the two cliche triangles of trig, yet this question does.

# cos ^2 theta + sin ^2 theta = 1 #

#cos ^2 theta = 1 - sin ^2 theta #

#cos theta = pm \sqrt{ 1 - sin ^2 theta }#

#cos theta = pm sqrt{ 1 - (-1/2)^2} = pm sqrt{3}/2 #

#tan theta = {sin theta}/{cos theta} = {-1/2}/{pm sqrt{3}/2}= pm 1/sqrt{3}#

Knowing only the sine, we cannot determine the sign of the cosine or of the tangent.

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