Cosine of 30 Degrees

Theorem

$\cos 30 \degrees = \cos \dfrac \pi 6 = \dfrac {\sqrt 3} 2$

where $\cos$ denotes the cosine.

$\ds \paren {\cos 30 \degrees}^2$

$=$

$\ds 1 - \paren {\sin 30 \degrees}^2$

$\ds $

$=$

$\ds 1 - \paren {\frac 1 2}^2$

$\ds $

$=$

$\ds \frac 3 4$

$\ds \leadsto \ \ $

$\ds \cos 30 \degrees$

$=$

$\ds \sqrt {\frac 3 4}$

$\ds $

$=$

$\ds \dfrac {\sqrt 3} 2$

positive because $\cos 30 \degrees$ is in Quadrant I

$\blacksquare$

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