Find the angle in degrees for which the $sin$ and $cos$ values are equal on the unit circle.

To find the angle $\theta$ in degrees for which $\sin(\theta) = \cos(\theta)$ on the unit circle, start by equating the two trigonometric functions:

$ \sin(\theta) = \cos(\theta) $

Divide both sides by $\cos(\theta)$ (where $\cos(\theta) \neq 0$):

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

So, the tangent function is:

$ \tan(\theta) = 1 $

The angle $\theta$ for which $\tan(\theta) = 1$ is:

$ \theta = 45^\circ $

To find the angle $ heta$ where $sin( heta) = cos( heta)$ on the unit circle:

$ sin( heta) = cos( heta) $

Divide both sides by $cos( heta)$:

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

Which implies that:

$ an( heta) = 1 $

The angle $ heta$ must be:

$ heta = 45^circ $

If $sin( heta) = cos( heta)$:

$ an( heta) = 1 $

Then:

$ heta = 45^circ $

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