Sine of 315 Degrees
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Theorem
- $\sin 315 \degrees = \sin \dfrac {7 \pi} 4 = -\dfrac {\sqrt 2} 2$
where $\sin$ denotes the sine function.
Proof
| \(\ds \sin 315 \degrees\) | \(=\) | \(\ds \map \sin {360 \degrees - 45 \degrees}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds -\sin 45 \degrees\) | Sine of Conjugate Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\dfrac {\sqrt 2} 2\) | Sine 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