Find the values of $sin( heta)$, $cos( heta)$, and $ an( heta)$ for $ heta = frac{pi}{4}$ using the unit circle

To find the values of $\sin(\theta)$, $\cos(\theta)$, and $\tan(\theta)$ for $\theta = \frac{\pi}{4}$ using the unit circle, we use the following:

On the unit circle, at $\theta = \frac{\pi}{4}$, the coordinates are: $(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})$.

So,

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

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

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

Using the unit circle, at $ heta = frac{pi}{4}$, the coordinates are: $(frac{1}{sqrt{2}}, frac{1}{sqrt{2}})$. Therefore:

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

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

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

The values are:

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

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

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

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