Tangent of 345 Degrees

Theorem

$\tan 345^\circ = \tan \dfrac {23 \pi} {12} = -\left({2 - \sqrt 3}\right)$

where $\tan$ denotes tangent.

Proof

\(\ds \tan 345^\circ\)

\(=\)

\(\ds \tan \left({360^\circ - 15^\circ}\right)\)

\(\ds \)

\(=\)

\(\ds -\tan 15^\circ\)

Tangent of Conjugate Angle

\(\ds \)

\(=\)

\(\ds -\left({2 - \sqrt 3}\right)\)

Tangent 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