Find the exact values of $ sin $ and $ cos $ for an angle of 225 degrees using the unit circle.

To find the exact values of $ \sin $ and $ \cos $ for an angle of 225 degrees using the unit circle, we first convert the angle to radians:

$ 225^\circ = 225 \times \frac{\pi}{180} = \frac{5\pi}{4} $

The angle \( \frac{5\pi}{4} \) is in the third quadrant, where both sine and cosine are negative.

For an angle of \( \frac{5\pi}{4} \), we can reference the unit circle to see that:

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

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

Hence, the exact values of sine and cosine for 225 degrees are:

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

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

To find the exact values of $ sin $ and $ cos $ for an angle of 225 degrees:

First convert to radians:

$ 225^circ = frac{5pi}{4} $

Since ( frac{5pi}{4} ) is in the third quadrant:

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

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

So:

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

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

Convert 225 degrees to radians:

$ 225^circ = frac{5pi}{4} $

In third quadrant:

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

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

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