Sine of Three Right Angles

From ProofWiki
Jump to navigation Jump to search

Theorem

$\sin 270 \degrees = \sin \dfrac {3 \pi} 2 = -1$

where $\sin$ denotes the sine function.


Proof

\(\ds \sin 270 \degrees\) \(=\) \(\ds \map \sin {360 \degrees - 90 \degrees}\)
\(\ds \) \(=\) \(\ds -\sin 90 \degrees\) Sine of Conjugate Angle
\(\ds \) \(=\) \(\ds -1\) Sine of Right Angle

$\blacksquare$


Also see


Sources