Cosine of 105 Degrees
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Theorem
- $\cos 105 \degrees = \cos \dfrac {7 \pi} {12} = - \dfrac {\sqrt 6 - \sqrt 2} 4$
where $\cos$ denotes cosine.
Proof
| \(\ds \cos 105 \degrees\) | \(=\) | \(\ds \map \cos {90 \degrees + 15 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\sin 15 \degrees\) | Cosine of Angle plus Right Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\frac {\sqrt 6 - \sqrt 2} 4\) | Sine of $15 \degrees$ |
$\blacksquare$
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