$ ext{Find the sine and cosine of } 135^circ ext{ using the unit circle.}$

$135^\circ$ is in the second quadrant. The reference angle is $180^\circ – 135^\circ = 45^\circ$.

The sine and cosine values for $45^\circ$ are $ \frac{1}{\sqrt{2}}$ and $\frac{1}{\sqrt{2}}$ respectively.

Since $135^\circ$ is in the second quadrant, the cosine value is negative and the sine value is positive.

Thus, $\cos 135^\circ = -\frac{1}{\sqrt{2}}$ and $\sin 135^\circ = \frac{1}{\sqrt{2}}$.

$135^circ$ is located in the second quadrant. The reference angle is $45^circ$ because $180^circ – 135^circ = 45^circ$.

We know that $sin 45^circ = frac{sqrt{2}}{2}$ and $cos 45^circ = frac{sqrt{2}}{2}$.

In the second quadrant, the cosine is negative and the sine is positive. Therefore,

$cos 135^circ = -frac{sqrt{2}}{2}$

$sin 135^circ = frac{sqrt{2}}{2}$

The angle $135^circ$ is in the second quadrant, where the reference angle is $45^circ$.

Hence, $cos 135^circ = -frac{sqrt{2}}{2}$ and $sin 135^circ = frac{sqrt{2}}{2}$.

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