Find the angle $ heta $ on the unit circle where the following conditions are met: $ sin( heta) = -frac{1}{2} $ and $ cos( heta) = -frac{sqrt{3}}{2} $

To find the angle $ \theta $ on the unit circle where $ \sin(\theta) = -\frac{1}{2} $ and $ \cos(\theta) = -\frac{\sqrt{3}}{2} $, we need to identify the corresponding angles in degrees.

First, note that $ \sin(\theta) = -\frac{1}{2} $ occurs at:

$ \theta = 210^\circ, 330^\circ $

Next, note that $ \cos(\theta) = -\frac{\sqrt{3}}{2} $ occurs at:

$ \theta = 150^\circ, 210^\circ $

The common angle is:

$ \theta = 210^\circ $

To find the angle $ heta $ on the unit circle where $ sin( heta) = -frac{1}{2} $ and $ cos( heta) = -frac{sqrt{3}}{2} $, we recognize the symmetry in the unit circle.

$ sin( heta) = -frac{1}{2} $ at angles:

$ 210^circ, 330^circ $

$ cos( heta) = -frac{sqrt{3}}{2} $ at angles:

$ 150^circ, 210^circ $

The intersection is:

$ heta = 210^circ $

Given $ sin( heta) = -frac{1}{2} $ and $ cos( heta) = -frac{sqrt{3}}{2} $, find $ heta $:

Common angle:

$ heta = 210^circ $

Start Using PopAi Today