Values of Sine for Standard Angles

The value of sine of an angle is a value, calculated from the ratio of length of the opposite side to length of the hypotenuse at the respective angle of the right angled triangle. The values of sine for different angles are derived geometrically but some of the sine values for some angles are usually used in mathematics.

Here is the list of sine values for standard angles, displayed in table in three angle measuring systems Sexagesimal, circular and centesimal systems. You can even learn how values of trigonometric ratio sine for standard angles are derived in mathematics by the geometric and algebraic approaches.

Angle ($\theta$) Sine value ($\sin \theta$)
Degrees Radians Gradians
$0^\circ$ $0$ $0^g$ $0$
$30^\circ$ $$\frac{\pi}{6}$$ $${33\frac{1}{3}}^g$$ $$\frac{1}{2}$$
$45^\circ$ $$\frac{\pi}{4}$$ $50^g$ $$\frac{1}{\sqrt{2}}$$
$60^\circ$ $$\frac{\pi}{3}$$ $${66\frac{2}{3}}^g$$ $$\frac{\sqrt{3}}{2}$$
$90^\circ$ $$\frac{\pi}{2}$$ $100^g$ $$1$$
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