Secant of Supplementary Angle
Theorem
- $\map \sec {\pi - \theta} = -\sec \theta$
where $\sec$ denotes secant.
That is, the secant of an angle is the negative of its supplement.
Proof
| \(\ds \map \sec {\pi - \theta}\) | \(=\) | \(\ds \frac 1 {\map \cos {\pi - \theta} }\) | Secant is Reciprocal of Cosine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \frac 1 {-\cos \theta}\) | Cosine of Supplementary Angle | |||||||||||
| \(\ds \) | \(=\) | \(\ds -\sec \theta\) | Secant is Reciprocal of Cosine |
$\blacksquare$
Also see
- Sine of Supplementary Angle
- Cosine of Supplementary Angle
- Tangent of Supplementary Angle
- Cotangent of Supplementary Angle
- Cosecant of Supplementary 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