Tangent Calculator

Easily calculate the tangent of an angle in degrees or radians. Visualize the result on the unit circle.

Enter Angle Details

Input the angle and select the unit (degrees or radians) to calculate the tangent.

Angle:

Unit:

Result:

Tangent of angle:

Tangent Visualization on Unit Circle

Understanding Tangent (tan)

In trigonometry, the tangent of an angle is the ratio of the sine to the cosine of the angle. It can also be visualized on a unit circle as the length of the vertical line segment tangent to the circle at the point where the terminal side of the angle intersects the circle, extending from the x-axis.

Formula:

$$ tan(\theta) = \frac{sin(\theta)}{cos(\theta)} $$

The tangent function has a period of π radians or 180 degrees, and it is undefined at angles where the cosine is zero (e.g., π/2, 3π/2 radians or 90°, 270° degrees).

Use Cases: Tangent is widely used in various fields such as:

Navigation and surveying
Physics (e.g., in mechanics and optics)
Engineering (e.g., in calculating slopes and angles in structural design)
Computer graphics and game development

For further reading, you can refer to resources like: Wikipedia - Tangent and MathWorld - Tangent.