Tangent of 135 Degrees
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Theorem
- $\tan 135^\circ = \tan \dfrac {3 \pi} 4 = - 1$
where $\tan$ denotes tangent.
Proof
| \(\ds \tan 135^\circ\) | \(=\) | \(\ds \tan \left({90^\circ + 45^\circ}\right)\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds - \cot 45^\circ\) | Tangent of Angle plus Right Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds - 1\) | Cotangent of 45 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