Secant of 60 Degrees
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Theorem
- $\sec 60 \degrees = \sec \dfrac \pi 3 = 2$
where $\sec$ denotes secant.
Proof
\(\ds \sec 60 \degrees\) | \(=\) | \(\ds \frac 1 {\cos 60 \degrees}\) | Secant is Reciprocal of Cosine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac 1 {\frac 1 2}\) | Cosine of $60 \degrees$ | |||||||||||
\(\ds \) | \(=\) | \(\ds 2\) | multiplying top and bottom by $2$ |
$\blacksquare$
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