How do you use use quotient identities to explain why the tangent and cotangent function have positive values for angles in the third quadrant?

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Answer 1 · 2014-11-05T10:56:31

If the terminal side of an angle #theta# is in the third quadrant, then

#pi < theta < {3pi}/2#,

which makes both #sin theta# and #cos theta# negative.

Since negative divided by negative is positive, both

#tan theta={sin theta}/{cos theta}# and #cot theta={cos theta}/{sin theta}#

are positive.

I hope that this was helpful.