Particular Values of Secant Function
Jump to navigation
Jump to search
Theorem
The following values of the secant function can be expressed as exact algebraic numbers.
This list is non-exhaustive.
Secant of Zero
- $\sec 0 = 0$
Secant of $15 \degrees$
- $\sec 15 \degrees = \sec \dfrac \pi {12} = \sqrt 6 - \sqrt 2$
Secant of $30 \degrees$
- $\sec 30 \degrees = \sec \dfrac \pi 6 = \dfrac {2 \sqrt 3} 3$
Secant of $45 \degrees$
- $\sec 45 \degrees = \sec \dfrac \pi 4 = \sqrt 2$
Secant of $60 \degrees$
- $\sec 60 \degrees = \sec \dfrac \pi 3 = 2$
Secant of $75 \degrees$
- $\sec 75 \degrees = \sec \dfrac {5 \pi} {12} = \sqrt 6 + \sqrt 2$
Secant of Right Angle
- $\sec 90 \degrees = \sec \dfrac \pi 2$ is undefined
Secant of $105 \degrees$
- $\sec 105 \degrees = \sec \dfrac {7 \pi} {12} = -\paren {\sqrt 6 + \sqrt 2}$
Secant of $120 \degrees$
- $\sec 120 \degrees = \sec \dfrac {2 \pi} 3 = -2$
Secant of $135 \degrees$
- $\sec 135 \degrees = \sec \dfrac {3 \pi} 4 = -\sqrt 2$
Secant of $150 \degrees$
- $\sec 150 \degrees = \sec \dfrac {5 \pi} 6 = -\dfrac {2 \sqrt 3} 3$
Secant of $165 \degrees$
- $\sec 165 \degrees = \sec \dfrac {11 \pi} {12} = -\paren {\sqrt 6 - \sqrt 2}$
Secant of Straight Angle
- $\sec 180 \degrees = \sec \pi = -1$
Secant of $195 \degrees$
- $\sec 195 \degrees = \sec \dfrac {13 \pi} {12} = -\paren {\sqrt 6 - \sqrt 2}$
Secant of $210 \degrees$
- $\sec 210 \degrees = \sec \dfrac {7 \pi} 6 = -2 \dfrac {\sqrt 3} 3$
Secant of $225 \degrees$
- $\sec 225 \degrees = \sec \dfrac {5 \pi} 4 = -\sqrt 2$
Secant of $240 \degrees$
- $\sec 240 \degrees = \sec \dfrac {4 \pi} 3 = - 2$
Secant of $255 \degrees$
- $\sec 255 \degrees = \sec \dfrac {17 \pi} {12} = -\paren {\sqrt 6 + \sqrt 2}$
Secant of Three Right Angles
- $\sec 270 \degrees = \sec \dfrac {3 \pi} 2$ is undefined
Secant of $285 \degrees$
- $\sec 285 \degrees = \sec \dfrac {19 \pi} {12} = \sqrt 6 + \sqrt 2$
Secant of $300 \degrees$
- $\sec 300 \degrees = \sec \dfrac {5 \pi} 3 = 2$
Secant of $315 \degrees$
- $\sec 315 \degrees = \sec \dfrac {7 \pi} 4 = \sqrt 2$
Secant of $330 \degrees$
- $\sec 330 \degrees = \sec \dfrac {11 \pi} 6 = 2 \dfrac {\sqrt 3} 3$
Secant of $345 \degrees$
- $\sec 345 \degrees = \sec \dfrac {23 \pi} {12} = \sqrt 6 - \sqrt 2$
Secant of Full Angle
- $\sec 360 \degrees = \sec 2 \pi = 1$
Also see
- Particular Values of Sine Function
- Particular Values of Cosine Function
- Particular Values of Tangent Function
- Particular Values of Cotangent Function
- Particular Values of Cosecant Function
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles