Sine of 60 Degrees
Theorem
- $\sin 60 \degrees = \sin \dfrac \pi 3 = \dfrac {\sqrt 3} 2$
where $\sin$ denotes the sine function.
Proof
| \(\ds \sin 60 \degrees\) | \(=\) | \(\ds \map \cos {90 \degrees - 60 \degrees}\) | Cosine of Complement equals Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \cos 30 \degrees\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {\sqrt 3} 2\) | Cosine of $30 \degrees$ |
$\blacksquare$
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
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): trigonometric function
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): trigonometric function
- 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