Sine of 150 Degrees

Theorem

$\sin 150 \degrees = \sin \dfrac {5 \pi} 6 = \dfrac 1 2$

where $\sin$ denotes the sine function.


Proof

\(\ds \sin 150 \degrees\) \(=\) \(\ds \map \sin {90 \degrees + 60 \degrees}\)
\(\ds \) \(=\) \(\ds \cos 60 \degrees\) Sine of Angle plus Right Angle
\(\ds \) \(=\) \(\ds \frac 1 2\) Cosine of $60 \degrees$

$\blacksquare$


Sources

  • 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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