Explain the coordinates of a point on the unit circle at an angle of $ frac{pi}{4} $

The unit circle is a circle with a radius of 1, centered at the origin (0, 0) in the coordinate plane. The coordinates of a point on the unit circle corresponding to an angle of $ \frac{\pi}{4} $ radians can be found using trigonometric functions.

At an angle of $ \frac{\pi}{4} $ radians, the x-coordinate and y-coordinate of the point are:

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

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

So the coordinates are:

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

The unit circle has a radius of 1. At an angle of $ frac{pi}{4} $, the coordinates of the point can be found using $ cos $ and $ sin $ functions:

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

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

Therefore, the coordinates are $(frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$

On the unit circle at $ frac{pi}{4} $, the coordinates are:

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

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