Sine of Right Angle
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Theorem
- $\sin 90 \degrees = \sin \dfrac \pi 2 = 1$
where $\sin$ denotes the sine function.
Proof
A direct implementation of Sine of Half-Integer Multiple of Pi:
- $\forall n \in \Z: \map \sin {n + \dfrac 1 2} \pi = \paren {-1}^n$
In this case, $n = 0$ and so:
- $\sin \dfrac 1 2 \pi = \paren {-1}^0 = 1$
$\blacksquare$
Also see
- Cosine of Right Angle
- Tangent of Right Angle
- Cotangent of Right Angle
- Secant of Right Angle
- Cosecant of Right Angle
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
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $12$: Trigonometric formulae: Trigonometric values for some special angles
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Appendix $14$: Trigonometric formulae: Trigonometric values for some special angles