medium

2 min read

Trigonometric values of standard degree angles

A trigonometric value of a standard degree angle is a ratio of the lengths of two sides of a right triangle with the length of the adjacent side. These ratios c...

A trigonometric value of a standard degree angle is a ratio of the lengths of two sides of a right triangle with the length of the adjacent side. These ratios can be used to find the sine, cosine, and tangent of any angle.

The standard degree angles are the angles that are formed by the intersection of two circles with radii of 1 unit. These angles include the angles for 0°, 30°, 45°, 60°, 75°, and 90°.

The trigonometric values of the standard degree angles are as follows:

$\sin0^\circ = 0$

$\cos0^\circ = 1$

$\tan0^\circ = 0$

$\sin30^\circ = \frac{1}{2}$

$\cos30^\circ = \frac{\sqrt{3}}{2}$

$\tan30^\circ = \frac{1}{3}$

$\sin45^\circ = \frac{\sqrt{2}}{2}$

$\cos45^\circ = \frac{\sqrt{2}}{2}$

$\tan45^\circ = 1$

$\sin60^\circ = \frac{\sqrt{3}}{2}$

$\cos60^\circ = \frac{1}{2}$

$\tan60^\circ = \frac{\sqrt{3}}{3}$

$\sin75^\circ = \frac{\sqrt{6}}{2}$

$\cos75^\circ = \frac{\sqrt{3}}{2}$

$\tan75^\circ = -\frac{\sqrt{3}}{3}$

$\sin90^\circ = 1$

$\cos90^\circ = 0$

$\tan90^\circ = undefined$

These values can be found using the following formulas:

$\sin x = \frac{opposite}{hypotenuse}$

$\cos x = \frac{adjacent}{hypotenuse}$

$\tan x = \frac{opposite}{adjacent}$

Trigonometric values can also be found using the unit circle. The unit circle is a circle with radius 1, and it is centered at the origin. The trigonometric values of the angles on the unit circle are the same as the trigonometric values of the standard degree angles