Find the coordinates of the point where the angle $frac{5pi}{4}$ radians intersects the unit circle.

First, we need to convert the angle $\frac{5\pi}{4}$ radians into degrees. We know that:

$ 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} $

Thus,

$ \frac{5\pi}{4} \text{ radians} = \frac{5\pi}{4} \times \frac{180}{\pi} \text{ degrees} = 225 \text{ degrees} $

On the unit circle, the coordinates corresponding to an angle of $225^{\circ}$ (or $\frac{5\pi}{4}$ radians) can be found using the cosine and sine functions:

$ \cos(225^{\circ}) = -\frac{\sqrt{2}}{2} $

$ \sin(225^{\circ}) = -\frac{\sqrt{2}}{2} $

Therefore, the coordinates are:

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

The given angle is $frac{5pi}{4}$ radians. To find the coordinates on the unit circle, we use the cosine and sine of that angle:

$ x = cosleft(frac{5pi}{4}
ight) $

$ y = sinleft(frac{5pi}{4}
ight) $

Knowing the unit circle properties:

$ cosleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

$ sinleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

So the coordinates are:

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

To find the coordinates at $frac{5pi}{4}$ radians on the unit circle:

$ cosleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

$ sinleft(frac{5pi}{4}
ight) = -frac{sqrt{2}}{2} $

Coordinates:

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

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