# Values of Trigonometric Ratios for Standard Angles

### Trigonometric Functions in Right Triangles

Sine:

The sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.

$\text{sine}=\frac{\text{length}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{of}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{leg}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{opposite}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{angle}}{\text{length}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{of}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{hypotenuse}}$

Cosine:

The cosine of an angle is the trigonometric ratio of the adjacent side to the hypotenuse of a right triangle containing that angle.

$\text{cosine}=\frac{\text{length}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{of}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{leg}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{adjacent}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{angle}}{\text{length}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{of}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{hypotenuse}}$

Tangent:

The tangent of an angle is the trigonometric ratio between the opposite side and the adjacent side of a right triangle containing that angle.

$\text{cosine}=\frac{\text{length}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{of}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{leg}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{opposite}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{angle}}{\text{length}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{of}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{leg}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{adjacent}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{the}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{angle}}$

### Trigonometric Values of Standard Angles

The following table gives the values of trigonometric ratios for standard angles.

$\begin{array}{|ccccccccc|}\hline \text{Degrees}& 0°& 30°& 45°& 60°& 90°& 180°& 270°& 360°\\ \text{Radians}& 0& \frac{\pi }{6}& \frac{\pi }{4}& \frac{\pi }{3}& \frac{\pi }{2}& \pi & \frac{3\pi }{2}& 2\pi \\ \text{Sine}& 0& \frac{1}{2}& \frac{\sqrt{2}}{2}& \frac{\sqrt{3}}{2}& 1& 0& -1& 0\\ \text{Cosine}& 1& \frac{\sqrt{3}}{2}& \frac{\sqrt{2}}{2}& \frac{1}{2}& 0& -1& 0& 1\\ \text{Tangent}& 0& \frac{\sqrt{3}}{3}& 1& \sqrt{3}& \text{undefined}& 0& \text{undefined}& 0\\ \hline\end{array}$

For more standard values, use the sine , cosine , and tangent pages.