Sine of 135 Degrees
Jump to navigation
Jump to search
Theorem
- $\sin 135 \degrees = \sin \dfrac {3 \pi} 4 = \dfrac {\sqrt 2} 2$
where $\sin$ denotes the sine function.
Proof
| \(\ds \sin 135 \degrees\) | \(=\) | \(\ds \map \sin {90 \degrees + 45 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \cos 45 \degrees\) | Sine of Angle plus Right Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {\sqrt 2} 2\) | Cosine 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