Cosine of Angle plus Right Angle

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Theorem

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


Proof

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

$\blacksquare$


Also see


Sources