Find the sine and cosine of the angle $ heta$ when it equals $pi/4$ on the unit circle.

To find the sine and cosine of the angle $\theta = \frac{\pi}{4}$ on the unit circle, we use the coordinates of the point where the terminal side of the angle intersects the unit circle.

The unit circle has a radius of 1, and for $\theta = \frac{\pi}{4}$, the coordinates are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$.

Therefore,

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

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

For $ heta = frac{pi}{4}$ on the unit circle, the sine and cosine values correspond to the coordinates of the point on the circle.

The unit circle equation is $x^2 + y^2 = 1$. At $ heta = frac{pi}{4}$, we have:

$x = cos left( frac{pi}{4}
ight)$

$y = sin left( frac{pi}{4}
ight)$

Thus, the point is $left( cos frac{pi}{4}, sin frac{pi}{4}
ight) = left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$. Hence,

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

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

At $ heta = frac{pi}{4}$, the unit circle coordinates are $left( frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$:

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

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

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