Cosecant of Three Right Angles less Angle
Theorem
- $\map \csc {\dfrac {3 \pi} 2 - \theta} = -\sec \theta$
where $\csc$ and $\sec$ are cosecant and secant respectively.
Proof
| \(\ds \map \csc {\frac {3 \pi} 2 - \theta}\) | \(=\) | \(\ds \frac 1 {\map \sin {\frac {3 \pi} 2 - \theta} }\) | Cosecant is Reciprocal of Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac 1 {-\cos \theta}\) | Sine of Three Right Angles less Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\sec \theta\) | Secant is Reciprocal of Cosine |
$\blacksquare$
Also see
- Sine of Three Right Angles less Angle
- Cosine of Three Right Angles less Angle
- Tangent of Three Right Angles less Angle
- Cotangent of Three Right Angles less Angle
- Secant of Three Right Angles less Angle
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Functions of Angles in All Quadrants in terms of those in Quadrant I