Sine of 225 Degrees
Jump to navigation
Jump to search
Theorem
- $\sin 225 \degrees = \sin \dfrac {5 \pi} 4 = -\dfrac {\sqrt 2} 2$
where $\sin$ denotes the sine function.
Proof
\(\ds \sin 225 \degrees\) | \(=\) | \(\ds \map \sin {360 \degrees - 135 \degrees}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds -\sin 135 \degrees\) | Sine of Conjugate Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds -\frac {\sqrt 2} 2\) | Sine of $135 \degrees$ |
$\blacksquare$
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