Find the value of $cosleft(frac{3pi}{4}
ight)$.

The unit circle helps us locate the angle $\theta = \frac{3\pi}{4}$ which lies in the second quadrant. The reference angle for $\theta = \frac{3\pi}{4}$ is:

$\pi – \frac{3\pi}{4} = \frac{\pi}{4}$

In the second quadrant, the cosine of an angle is negative:

$\cos\left(\frac{3\pi}{4}\right) = -\cos\left(\frac{\pi}{4}\right)$

Since $\cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$, we have:

$\cos\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2}$

To find $cosleft(frac{3pi}{4}
ight)$, locate the angle on the unit circle. The reference angle is $frac{pi}{4}$. In the second quadrant, cosine is negative:

$cosleft(frac{3pi}{4}
ight) = -cosleft(frac{pi}{4}
ight) = -frac{sqrt{2}}{2}$

$cosleft(frac{3pi}{4}
ight) = -frac{sqrt{2}}{2}$

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