# Evaluate \sin\frac{\pi}{4}.

Evaluate $$\displaystyle{\sin{{\frac{{\pi}}{{{4}}}}}}$$.

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Jonathan Burroughs
By the Pythogoras theorem:
$$\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={1}$$
so, if x=y, we will have:
$$\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={1}$$
$$\displaystyle{2}{y}^{{{2}}}={1}$$
$$\displaystyle{y}^{{{2}}}={\frac{{{1}}}{{{2}}}}$$
$$\displaystyle{y}=\sqrt{{{\frac{{{1}}}{{{2}}}}}}={\frac{{\sqrt{{{2}}}}}{{{2}}}}$$
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ambarakaq8

$$\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={1}$$
$$\displaystyle{2}{y}^{{{2}}}={1}$$
$$\displaystyle{y}^{{{2}}}={\frac{{{1}}}{{{2}}}}$$
$$\displaystyle{y}=\sqrt{{{\frac{{{1}}}{{{2}}}}}}$$
$$\displaystyle{y}={\frac{{\sqrt{{{2}}}}}{{{2}}}}$$
RizerMix

$$\frac{\sqrt{2}}{2}$$ is the answer.