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