Cosine of 285 Degrees

Theorem

$\cos 285^\circ = \cos \dfrac {19 \pi} {12} = \dfrac {\sqrt 6 - \sqrt 2} 4$

where $\cos$ denotes cosine.

Proof

\(\ds \cos 285^\circ\)

\(=\)

\(\ds \cos \left({360^\circ - 75^\circ}\right)\)

\(\ds \)

\(=\)

\(\ds \cos 75^\circ\)

Cosine of Conjugate Angle

\(\ds \)

\(=\)

\(\ds \frac {\sqrt 6 - \sqrt 2} 4\)

Cosine of 75 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