If $ heta$ is an angle in the unit circle such that $cos( heta) = frac{1}{2}$ and $sin( heta) = frac{sqrt{3}}{2}$, find the value of $ heta$ in degrees and radians.

To solve this problem, we need to determine the angle $\theta$ on the unit circle. Given:

$\cos(\theta) = \frac{1}{2}$ $\sin(\theta) = \frac{\sqrt{3}}{2}$

On the unit circle, these values correspond to the angle $\theta = 60^{\circ}$ or $\theta = \frac{\pi}{3}$ radians.

Therefore, the value of $\theta$ is:

$\theta = 60^{\circ}$ $\theta = \frac{\pi}{3}$

First, identify the quadrant where both $cos( heta) = frac{1}{2}$ and $sin( heta) = frac{sqrt{3}}{2}$ are true. This corresponds to the first quadrant where both sine and cosine are positive.

The angle $ heta$ that satisfies these conditions is:

$ heta = 60^{circ}$ $ heta = frac{pi}{3}$

Thus,

$ heta = 60^{circ}$ $ heta = frac{pi}{3}$

We are given:

$cos( heta) = frac{1}{2}$ $sin( heta) = frac{sqrt{3}}{2}$

These values occur at:

$ heta = 60^{circ} = frac{pi}{3}$

Start Using PopAi Today