Cosecant of 45 Degrees
Theorem
- $\csc 45^\circ = \csc \dfrac \pi 4 = \sqrt 2$
where $\csc$ denotes cosecant.
Proof
| \(\ds \csc 45^\circ\) | \(=\) | \(\ds \frac 1 {\sin 45^\circ}\) | Cosecant is Reciprocal of Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac 1 {\frac {\sqrt 2} 2}\) | Sine of 45 Degrees | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sqrt 2\) | multiplying top and bottom by $2 \sqrt 2$ |
$\blacksquare$
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