In which quadrant is cotangent positive?

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Answer 1 · 2015-06-13T10:26:48

QI and QIII

In QI: $0 < θ < \frac{π}{2}$ $0 < theta < pi/2$ then $sin θ > 0$ $sin theta > 0$ and $cos θ > 0$ $cos theta > 0$

so $cot θ = \frac{cos θ}{sin θ} > 0$ $cot theta = (cos theta) / (sin theta) > 0$

In QIII: $π < θ < \frac{3 π}{2}$ $pi < theta < (3pi)/2$ then $sin θ < 0$ $sin theta < 0$ and $cos θ < 0$ $cos theta < 0$

so $cot θ = \frac{cos θ}{sin θ} > 0$ $cot theta = (cos theta) / (sin theta) > 0$

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

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.