Question

which quarters of the unit circle satisfy the trigonometric inequality tanθ≤0? assume that θ is the angle made by the positive x - axis and a ray from the origin. the top right and bottom right quarters the top right and bottom left quarters the top left and bottom right quarters the top left and bottom left quarters

Explanation:

Step1: Recall tangent formula

$\tan\theta=\frac{\sin\theta}{\cos\theta}$

Step2: Analyze sign - rules

$\tan\theta\leq0$ when $\sin\theta$ and $\cos\theta$ have opposite signs.

Step3: Determine quadrants

In the second quadrant (top - left), $\sin\theta> 0,\cos\theta<0$; in the fourth quadrant (bottom - left), $\sin\theta<0,\cos\theta>0$. So the quadrants where $\tan\theta\leq0$ are the top left and bottom left quarters.

Answer:

The top left and bottom left quarters