Question

which half of the unit circle satisfies the trigonometric inequality cos θ>0? assume that θ 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 $(x,y)$ with angle $\theta$ made by the positive $x$ - axis and the ray from the origin to the point, $\cos\theta=x$.

Step2: Determine where $\cos\theta<0$

We want to find where $x < 0$. In the coordinate system, the $x$ - values are negative in the left - hand half of the unit - circle (where the angle $\theta$ satisfies $\frac{\pi}{2}<\theta<\frac{3\pi}{2}$ in radians or $90^{\circ}<\theta<270^{\circ}$ in degrees).

Answer:

The left - hand half