Sine of Three Right Angles
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Theorem
- $\sin 270 \degrees = \sin \dfrac {3 \pi} 2 = -1$
where $\sin$ denotes the sine function.
Proof
\(\ds \sin 270 \degrees\) | \(=\) | \(\ds \map \sin {360 \degrees - 90 \degrees}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds -\sin 90 \degrees\) | Sine of Conjugate Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds -1\) | Sine of Right Angle |
$\blacksquare$
Also see
- Cosine of Three Right Angles
- Tangent of Three Right Angles
- Cotangent of Three Right Angles
- Secant of Three Right Angles
- Cosecant of Three Right Angles
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Special angles
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles