Cosine of 75 Degrees
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Theorem
- $\cos 75^\circ = \cos \dfrac {5 \pi}{12} = \dfrac {\sqrt 6 - \sqrt 2} 4$
where $\cos$ denotes the cosine.
Proof
| \(\ds \cos 75^\circ\) | \(=\) | \(\ds \cos \left({90^\circ - 15^\circ}\right)\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \sin 15^\circ\) | Cosine of Complement equals Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {\sqrt 6 - \sqrt 2} 4\) | Sine of $15^\circ$ |
$\blacksquare$
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