Determine the coordinates of the points on the unit circle where the angle is $ frac{pi}{4} $

To determine the coordinates of the points on the unit circle where the angle is $ \frac{\pi}{4} $, we need to use trigonometric functions.

On the unit circle, the x-coordinate is given by $ \cos(\theta) $ and the y-coordinate is given by $ \sin(\theta) $, where $ \theta $ is the angle.

For $ \theta = \frac{\pi}{4} $:

$ x = \cos\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} $

$ y = \sin\left(\frac{\pi}{4}\right) = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2} $

Thus, the coordinates are:

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

To find the points on the unit circle for $ frac{pi}{4} $, use:

$ x = cosleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2} $

$ y = sinleft(frac{pi}{4}
ight) = frac{sqrt{2}}{2} $

Coordinates: $ left(frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight) $

For $ frac{pi}{4} $, the coordinates are:

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

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