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