Cotangent of 135 Degrees
Jump to navigation
Jump to search
Theorem
- $\cot 135 \degrees = \cot \dfrac {3 \pi} 4 = -1$
where $\cot$ denotes cotangent.
Proof
| \(\ds \cot 135 \degrees\) | \(=\) | \(\ds \cot \paren {90 \degrees + 45 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\tan 45 \degrees\) | Cotangent of Angle plus Right Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds - 1\) | Tangent 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