Find the point(s) where the derivative of $ cos( heta) $ equals zero on the filled out unit circle

To find where the derivative of $ \cos(\theta) $ equals zero, we first need to find the derivative:

$ \frac{d}{d\theta} \cos(\theta) = -\sin(\theta) $

Set the derivative to zero:

$ -\sin(\theta) = 0 $

Thus, we have:

$ \sin(\theta) = 0 $

The solutions to this equation on the unit circle are:

$ \theta = 0, \pi, 2\pi $

Therefore, the points on the unit circle are:

$ (1, 0), (-1, 0), (1, 0) $

To locate the points where the derivative of $ cos( heta) $ is zero, we calculate:

$ frac{d}{d heta} cos( heta) = -sin( heta) $

Set it equal to zero:

$ -sin( heta) = 0 $

This simplifies to:

$ sin( heta) = 0 $

On the unit circle, the values are:

$ heta = 0, pi, 2pi $

The points corresponding to these values are:

$ (1, 0), (-1, 0), (1, 0) $

To find where the derivative of $ cos( heta) $ equals zero:

$ frac{d}{d heta} cos( heta) = -sin( heta) $

Setting it to zero:

$ -sin( heta) = 0 $

Solutions on the unit circle:

$ heta = 0, pi, 2pi $

Points are:

$ (1, 0), (-1, 0), (1, 0) $

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