Find the coordinates of the point on the unit circle corresponding to an angle of $ frac{pi}{4} $

To find the coordinates of the point on the unit circle corresponding to an angle of $ \frac{\pi}{4} $, we use the unit circle definition:

The unit circle equation is: $ x^2 + y^2 = 1 $

At an angle of $ \frac{\pi}{4} $, both cosine and sine values are equal. Hence:

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

To find the coordinates at an angle of $ frac{pi}{4} $ on the unit circle:

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

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

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

Coordinates at $ frac{pi}{4} $ are:

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

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