Secant of Conjugate Angle
Jump to navigation
Jump to search
Theorem
- $\map \sec {2 \pi - \theta} = \sec \theta$
where $\sec$ denotes secant.
That is, the secant of an angle equals its conjugate.
Proof
\(\ds \map \sec {2 \pi - \theta}\) | \(=\) | \(\ds \frac 1 {\map \cos {2 \pi - \theta} }\) | Secant is Reciprocal of Cosine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac 1 {\cos \theta}\) | Cosine of Conjugate Angle | |||||||||||
\(\ds \) | \(=\) | \(\ds \sec \theta\) | Secant is Reciprocal of Cosine |
$\blacksquare$
Examples
Secant of $360 \degrees - 3 x$
- $\map \sec {360 \degrees - 3 x} = \sec 3 x$
Also see
- Sine of Conjugate Angle
- Cosine of Conjugate Angle
- Tangent of Conjugate Angle
- Cotangent of Conjugate Angle
- Cosecant of Conjugate 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