In which quadrant is cotangent positive?

Question

14660 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-13T10:26:48

QI and QIII

In QI: $0 < theta < pi/2$ then $sin theta > 0$ and $cos theta > 0$

so $cot theta = (cos theta) / (sin theta) > 0$

In QIII: $pi < theta < (3pi)/2$ then $sin theta < 0$ and $cos theta < 0$

so $cot theta = (cos theta) / (sin theta) > 0$

In QII and QIV $sin$ and $cos$ have opposite signs and $cot < 0$

Answer 2 · 2015-06-13T18:56:25

Find quadrants where cots are positive

On the trig unit circle, Quadrant I and Quadrant III have cots positive.