Find the coordinates of the point on the unit circle at an angle of $frac{5pi}{4}$ radians.

To find the coordinates of the point on the unit circle at an angle of $\frac{5\pi}{4}$ radians, we can use the cosine and sine functions:

$ x = \cos \left( \frac{5\pi}{4} \right) $

$ y = \sin \left( \frac{5\pi}{4} \right) $

First, let’s calculate the cosine value:

$ \cos \left( \frac{5\pi}{4} \right) = -\frac{\sqrt{2}}{2} $

Next, let’s calculate the sine value:

$ \sin \left( \frac{5\pi}{4} \right) = -\frac{\sqrt{2}}{2} $

Therefore, the coordinates of the point are:

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

Given an angle $frac{5pi}{4}$ radians on the unit circle, we can determine the coordinates by using the properties of the unit circle.

We evaluate the cosine and sine of the angle:

$ x = cos left( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

$ y = sin left( frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

Thus, the coordinates at $frac{5pi}{4}$ radians are:

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

The coordinates at $frac{5pi}{4}$ radians on the unit circle are:

$ left( cos left( frac{5pi}{4}
ight), sin left( frac{5pi}{4}
ight)
ight) = left( -frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight) $

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