Sine of Three Right Angles

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

  • 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Special angles
  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles
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