tan30

The tangent of 30 degrees, denoted as tan(30°), is a fundamental trigonometric ratio that represents the ratio of the length of the opposite side to the adjacent side in a right-angled triangle with a 30-degree angle. It is one of the standard trigonometric values that are commonly memorized in mathematics.

The exact value of tan(30°) is 1/√3, which can also be expressed as √3/3 after rationalizing the denominator. This value is derived from the properties of a 30-60-90 right triangle, where the sides are in the ratio 1:√3:2.

In decimal form, tan(30°) is approximately equal to 0.57735. This value is used extensively in various mathematical applications, including geometry, physics, and engineering.

The tangent function has a period of 180 degrees, meaning tan(30°) = tan(210°) = tan(390°), and so on. Additionally, tan(30°) is related to other trigonometric functions through identities, such as tan(30°) = sin(30°)/cos(30°).

This value is particularly important in fields that require calculations involving angles and triangles, such as surveying, navigation, and architecture.