Find the sine, cosine, and tangent values for the angle $frac{pi}{4}$ on the unit circle

First, we need to recognize that the angle $\frac{\pi}{4}$ is equivalent to 45 degrees.

On the unit circle, the coordinates at $\frac{\pi}{4}$ are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$.

The sine value is the y-coordinate:

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

The cosine value is the x-coordinate:

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

The tangent value is the ratio of the sine and cosine values:

$\tan(\frac{\pi}{4}) = \frac{\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{4})} = 1$

So, the sine, cosine, and tangent values for the angle $\frac{\pi}{4}$ are $\frac{\sqrt{2}}{2}$, $\frac{\sqrt{2}}{2}$, and 1, respectively.

We start by noting that $frac{pi}{4}$ radians is 45 degrees.

At this angle on the unit circle, the coordinates are $(frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$.

The sine value is given by the y-coordinate:

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

The cosine value is given by the x-coordinate:

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

The tangent value is the division of the sine by the cosine:

$ an(frac{pi}{4}) = frac{frac{sqrt{2}}{2}}{frac{sqrt{2}}{2}} = 1$

Therefore, the sine, cosine, and tangent values are $frac{sqrt{2}}{2}$, $frac{sqrt{2}}{2}$, and 1, respectively.

The angle $frac{pi}{4}$ on the unit circle corresponds to the point $(frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$.

Thus,

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

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

$ an(frac{pi}{4}) = 1$

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