Particular Values of Tangent Function
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Theorem
The following values of the tangent function can be expressed as exact algebraic numbers.
This list is non-exhaustive.
Tangent of Zero
- $\tan 0 = 0$
Tangent of 15 Degrees
- $\tan 15^\circ = \tan \dfrac {\pi} {12} = 2 - \sqrt 3$
Tangent of 22.5 Degrees
- $\tan 22.5 \degrees = \tan \dfrac \pi 8 = \sqrt 2 - 1$
Tangent of 30 Degrees
- $\tan 30 \degrees = \tan \dfrac \pi 6 = \dfrac {\sqrt 3} 3$
Tangent of 45 Degrees
- $\tan 45 \degrees = \tan \dfrac \pi 4 = 1$
Tangent of 60 Degrees
- $\tan 60 \degrees = \tan \dfrac \pi 3 = \sqrt 3$
Tangent of 67.5 Degrees
- $\tan 67.5 \degrees = \tan \dfrac {3 \pi} 8 = \sqrt 2 + 1$
Tangent of 75 Degrees
- $\tan 75 \degrees = \tan \dfrac {5 \pi} {12} = 2 + \sqrt 3$
Tangent of Right Angle
- $\tan 90 \degrees = \tan \dfrac \pi 2$ is undefined
Tangent of 105 Degrees
- $\tan 105^\circ = \tan \dfrac {7 \pi} {12} = - \left({2 + \sqrt 3}\right)$
Tangent of 120 Degrees
- $\tan 120 \degrees = \tan \dfrac {2 \pi} 3 = -\sqrt 3$
Tangent of 135 Degrees
- $\tan 135^\circ = \tan \dfrac {3 \pi} 4 = - 1$
Tangent of 150 Degrees
- $\tan 150 \degrees = \tan \dfrac {5 \pi} 6 = -\dfrac {\sqrt 3} 3$
Tangent of 165 Degrees
- $\tan 165 \degrees = \tan \dfrac {11 \pi} {12} = -\paren {2 - \sqrt 3}$
Tangent of Straight Angle
- $\tan 180 \degrees = \tan \pi = 0$
Tangent of 195 Degrees
- $\tan 195 \degrees = \tan \dfrac {13 \pi} {12} = 2 - \sqrt 3$
Tangent of 210 Degrees
- $\tan 210 \degrees = \tan \dfrac {7 \pi} 6 = \dfrac {\sqrt 3} 3$
Tangent of 225 Degrees
- $\tan 225 \degrees = \tan \dfrac {5 \pi} 4 = 1$
Tangent of 240 Degrees
- $\tan 240 \degrees = \tan \dfrac {4 \pi} 3 = \sqrt 3$
Tangent of 255 Degrees
- $\tan 255 \degrees = \tan \dfrac {17 \pi} {12} = 2 + \sqrt 3$
Tangent of Three Right Angles
- $\tan 270 \degrees = \tan \dfrac {3 \pi} 2$ is undefined
Tangent of 285 Degrees
- $\tan 285 \degrees = \tan \dfrac {19 \pi} {12} = -\paren {2 + \sqrt 3}$
Tangent of 300 Degrees
- $\tan 300 \degrees = \tan \dfrac {5 \pi} 3 = -\sqrt 3$
Tangent of 315 Degrees
- $\tan 315 \degrees = \tan \dfrac {7 \pi} 4 = -1$
Tangent of 330 Degrees
- $\tan 330^\circ = \tan \dfrac {11 \pi} 6 = -\dfrac {\sqrt 3} 3$
Tangent of 345 Degrees
- $\tan 345^\circ = \tan \dfrac {23 \pi} {12} = -\left({2 - \sqrt 3}\right)$
Tangent of Full Angle
- $\tan 360^\circ = \tan 2 \pi = 0$
Also see
- Particular Values of Sine Function
- Particular Values of Cosine Function
- Particular Values of Cotangent 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