Find the angle in the unit circle

Given a point on the unit circle, find the angle such that $\sin(\theta) = \frac{\sqrt{3}}{2}$ and $\cos(\theta) = \frac{1}{2}$.

First, recognize that the coordinates given correspond to the point $(\frac{1}{2}, \frac{\sqrt{3}}{2})$ on the unit circle.

This point is in the first quadrant, where all trigonometric functions are positive.

The angle $\theta$ which satisfies this condition is $\theta = \frac{\pi}{3}$.

Therefore, the angle is $\theta = \frac{\pi}{3}$.

Given the point on the unit circle where $ an( heta) = 1$ and $sin( heta) = cos( heta)$, find the angle $ heta$.

Since $ an( heta) = frac{sin( heta)}{cos( heta)}$, and we have $ an( heta) = 1$, it follows that $sin( heta) = cos( heta)$.

The angle $ heta$ where this is true in the first quadrant is $ heta = frac{pi}{4}$.

Therefore, the angle is $ heta = frac{pi}{4}$.

Determine the angle $ heta$ on the unit circle for which $sin( heta) = frac{1}{2}$ and $cos( heta) = frac{sqrt{3}}{2}$.

Using the known values from the unit circle, the angle $ heta$ is $ heta = frac{pi}{6}$.

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