$ ext{Conversion Problem on the Unit Circle}$

$\text{Given that } \theta = \frac{5\pi}{4} \text{ radians}, \text{ convert this angle to degrees and then determine the coordinates of the corresponding point on the unit circle.}$

$\text{To convert radians to degrees, use the formula:}$

$\theta_{deg} = \theta_{rad} \times \frac{180^{\circ}}{\pi}$

$\theta_{deg} = \frac{5\pi}{4} \times \frac{180^{\circ}}{\pi}$

$\theta_{deg} = 225^{\circ}$

$\text{Next, find the coordinates on the unit circle for } 225^{\circ}. \text{ This corresponds to the angle } 225^{\circ} \text{ or } \frac{5\pi}{4} \text{ radians.}$

$\cos(225^{\circ}) = \cos\left(\frac{5\pi}{4}\right) = -\frac{\sqrt{2}}{2}$

$\sin(225^{\circ}) = \sin\left(\frac{5\pi}{4}\right) = -\frac{\sqrt{2}}{2}$

$\text{Therefore, the coordinates are: } \left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$

$ ext{Given that } heta = frac{5pi}{4} ext{ radians}, ext{ convert this angle to degrees and find the point on the unit circle.}$

$ heta_{deg} = heta_{rad} imes frac{180^{circ}}{pi}$

$ heta_{deg} = frac{5pi}{4} imes frac{180^{circ}}{pi}$

$ heta_{deg} = 225^{circ}$

$ ext{Coordinates: } cos(225^{circ}) = -frac{sqrt{2}}{2}, sin(225^{circ}) = -frac{sqrt{2}}{2}$

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

$ heta = frac{5pi}{4} ext{ radians}$

$ heta_{deg} = frac{5pi}{4} imes frac{180^{circ}}{pi} = 225^{circ}$

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

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

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