Given a point on the unit circle, find the corresponding angle $ heta $ and verify the coordinates

Let

Consider the point $(frac{1}{2}, frac{sqrt{3}}{2})$ on the unit circle.

This corresponds to the angle $ heta $ where:

$ cos( heta) = frac{1}{2} $

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

From trigonometric values,:

$ heta = frac{pi}{3} $

Verification:

$ cos(frac{pi}{3}) = frac{1}{2} $

$ sin(frac{pi}{3}) = frac{sqrt{3}}{2} $

Thus, coordinates are correct.

Given point: $(frac{1}{2}, frac{sqrt{3}}{2})$

Find angle:

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

Angle: $ heta = frac{pi}{3} $

Verification:

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

Start Using PopAi Today