Sine of Angle plus Right Angle

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Theorem

$\sin \paren {x + \dfrac \pi 2} = \cos x$


Proof

\(\displaystyle \sin \paren {x + \frac \pi 2}\) \(=\) \(\displaystyle \sin x \cos \frac \pi 2 + \cos x \sin \frac \pi 2\) Sine of Sum
\(\displaystyle \) \(=\) \(\displaystyle \sin x \cdot 0 + \cos x \cdot 1\) Cosine of Right Angle and Sine of Right Angle
\(\displaystyle \) \(=\) \(\displaystyle \cos x\)

$\blacksquare$


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Sources