Cosecant of Angle plus Three Right Angles
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Theorem
- $\map \csc {x + \dfrac {3 \pi} 2} = -\sec x$
Proof
\(\ds \map \csc {x + \frac {3 \pi} 2}\) | \(=\) | \(\ds \frac 1 {\map \sin {x + \frac {3 \pi} 2} }\) | Cosecant is Reciprocal of Sine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac 1 {-\cos x}\) | Sine of Angle plus Three Right Angles | |||||||||||
\(\ds \) | \(=\) | \(\ds -\sec x\) | Secant is Reciprocal of Cosine |
$\blacksquare$
Also see
- Sine of Angle plus Three Right Angles
- Cosine of Angle plus Three Right Angles
- Tangent of Angle plus Three Right Angles
- Cotangent of Angle plus Three Right Angles
- Secant of Angle plus Three Right Angles
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