Find the coordinates where $ cos( heta) = sin( heta) $ on the unit circle

To find the coordinates where $ \cos(\theta) = \sin(\theta) $ on the unit circle, we start from the equation:

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

Since both cosine and sine are equal, we can express this as:

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

Divide both sides by $ \cos(\theta) $:

$1 = \tan(\theta) $

This implies

$ \theta = \frac{\pi}{4} + n\pi $

for integer values of n. The corresponding coordinates on the unit circle are:

$ \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) $ and $ \left( -\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2} \right) $

To find the points where $ cos( heta) = sin( heta) $ on the unit circle, we use:

$ cos( heta) = sin( heta) $

This simplifies to:

$1 = an( heta) $

or:

$ heta = frac{pi}{4} + npi $

Hence, points are:

$ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $ and $ left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight) $

Where $ cos( heta) = sin( heta) $ on the unit circle:

$ heta = frac{pi}{4} + npi $

Coordinates:

$ left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $ and $ left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight) $

Start Using PopAi Today