Find the sine and cosine values of $frac{pi}{4}$ using the unit circle.

To find the sine and cosine values of $\frac{\pi}{4}$ using the unit circle, follow these steps:

1. Identify the angle $\frac{\pi}{4}$ on the unit circle. This angle corresponds to 45 degrees.

2. For the angle $\frac{\pi}{4}$, both the x-coordinate (cosine) and the y-coordinate (sine) of the point on the unit circle are equal.

3. Using the symmetry of the unit circle, the sine and cosine values for $\frac{\pi}{4}$ are:

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

So, the sine and cosine values of $\frac{\pi}{4}$ are both $\frac{\sqrt{2}}{2}$.

To determine the sine and cosine of $frac{pi}{4}$ using the unit circle, proceed as follows:

1. Locate the angle $frac{pi}{4}$ on the unit circle. This angle represents 45 degrees.

2. The coordinates of the corresponding point on the circle are found by the cosine (x-coordinate) and sine (y-coordinate) values.

3. For $frac{pi}{4}$, these coordinates are:

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

Therefore, both cosine and sine of $frac{pi}{4}$ are $frac{sqrt{2}}{2}$.

To find the sine and cosine of $frac{pi}{4}$:

1. Find $frac{pi}{4}$ on the unit circle (45 degrees).

2. Coordinates are:

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

So, the values are $frac{sqrt{2}}{2}$.

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