If cos theta = 5/13, theta in quadrant II, how do you find sin theta and tan theta?

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Answer 1 · 2016-06-13T22:33:22

#cos theta < 0# in Q2, so there is no answer, but read on...

If #theta# were in Q1 then we would simply be dealing with the internal angles of a #5#, #12#, #13# right angled triangle.

Note that:

#5^2+12^2 = 25+144 = 169 = 13^2#

Hence in Q1 we would have:

#sin theta = 12/13# and #tan theta = 12/5#

In Q2, #cos theta < 0#, so cannot be equal to #5/13#, so there is an error in the question.

In Q4, we would find #sin theta = -12/13# and #tan theta = -12/5#.

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