Question

which half of the unit circle satisfies the trigonometric inequality unclear symbol > 0? assume that unclear symbol is the angle made by the positive x - axis and a ray from the origin. the top half the bottom half the right half the left half

Explanation:

Step1: Recall cosine definition on unit - circle

On the unit - circle, for a point $(x,y)$ corresponding to an angle $\theta$ made by the positive $x$ - axis and a ray from the origin, $\cos\theta=x$.

Step2: Analyze cosine values in different halves

In the right - half of the unit - circle ($-\frac{\pi}{2}<\theta<\frac{\pi}{2}$), $x>0$ (since $x = \cos\theta$), so $\cos\theta>0$. In the left - half of the unit - circle ($\frac{\pi}{2}<\theta<\frac{3\pi}{2}$), $x < 0$, so $\cos\theta<0$. If the inequality is $\cos\theta<0$, the left - half of the unit - circle satisfies it.

Answer:

D. the left half