Particular Values of Cotangent Function
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Theorem
The following values of the cotangent function can be expressed as exact algebraic numbers.
This list is non-exhaustive.
Cotangent of Zero
- $\cot 0$ is undefined
Cotangent of 15 Degrees
- $\cot 15 \degrees = \cot \dfrac {\pi} {12} = 2 + \sqrt 3$
Cotangent of 30 Degrees
- $\cot 30 \degrees = \cot \dfrac \pi 6 = \sqrt 3$
Cotangent of 45 Degrees
- $\cot 45 \degrees = \cot \dfrac \pi 4 = 1$
Cotangent of 60 Degrees
- $\cot 60 \degrees = \cot \dfrac \pi 3 = \dfrac {\sqrt 3} 3$
Cotangent of 75 Degrees
- $\cot 75 \degrees = \cot \dfrac {5 \pi} {12} = 2 - \sqrt 3$
Cotangent of Right Angle
- $\cot 90 \degrees = \cot \dfrac \pi 2 = 0$
Cotangent of 105 Degrees
- $\cot 105^\circ = \cot \dfrac {7 \pi} {12} = -\left({2 - \sqrt 3}\right)$
Cotangent of 120 Degrees
- $\cot 120 \degrees = \cot \dfrac {2 \pi} 3 = -\dfrac {\sqrt 3} 3$
Cotangent of 135 Degrees
- $\cot 135 \degrees = \cot \dfrac {3 \pi} 4 = -1$
Cotangent of 150 Degrees
- $\cot 150 \degrees = \cot \dfrac {5 \pi} 6 = -\sqrt 3$
Cotangent of 165 Degrees
- $\cot 165 \degrees = \cot \dfrac {11 \pi} {12} = -\paren {2 + \sqrt 3}$
Cotangent of Straight Angle
- $\cot 180^\circ = \cot \pi$ is undefined
Cotangent of 195 Degrees
- $\cot 195 \degrees = \cot \dfrac {13 \pi} {12} = 2 + \sqrt 3$
Cotangent of 210 Degrees
- $\cot 210^\circ = \cot \dfrac {7 \pi} 6 = \sqrt 3$
Cotangent of 225 Degrees
- $\cot 225^\circ = \cot \dfrac {5 \pi} 4 = 1$
Cotangent of 240 Degrees
- $\cot 240^\circ = \cot \dfrac {4 \pi} 3 = \dfrac {\sqrt 3} 3$
Cotangent of 255 Degrees
- $\cot 255 \degrees = \cot \dfrac {17 \pi} {12} = 2 - \sqrt 3$
Cotangent of Three Right Angles
- $\cot 270 \degrees = \cot \dfrac {3 \pi} 2 = 0$
Cotangent of 285 Degrees
- $\cot 285 \degrees = \cot \dfrac {19 \pi} {12} = -\paren {2 - \sqrt 3}$
Cotangent of 300 Degrees
- $\cot 300 \degrees = \cot \dfrac {5 \pi} 3 = - \dfrac {\sqrt 3} 3$
Cotangent of 315 Degrees
- $\cot 315 \degrees = \cot \dfrac {7 \pi} 4 = -1$
Cotangent of 330 Degrees
- $\cot 330^\circ = \cot \dfrac {11 \pi} 6 = -\sqrt 3$
Cotangent of 345 Degrees
- $\cot 345 \degrees = \cot \dfrac {23 \pi} {12} = -\paren {2 + \sqrt 3}$
Cotangent of Full Angle
- $\cot 360^\circ = \cot 2 \pi$ is undefined
Also see
- Particular Values of Sine Function
- Particular Values of Cosine Function
- Particular Values of Tangent Function
- Particular Values of Secant 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