Tangent Calculator

How to Calculate Tangent

The tangent function, denoted as tan(x), is a fundamental trigonometric function that relates the angles of a right triangle to the ratios of the lengths of its sides. It is widely used in various fields of mathematics, physics, and engineering.

Formula

The tangent of an angle θ in a right-angled triangle is defined as:

\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{\sin(\theta)}{\cos(\theta)} \]

Where:

• tan(θ) is the tangent of the angle θ
• opposite is the length of the side opposite to the angle θ
• adjacent is the length of the side adjacent to the angle θ
• θ is the angle in radians

Calculation Steps

1. Ensure the angle is in radians. If it's in degrees, convert it to radians by multiplying by π/180°.
2. Use a calculator or trigonometric tables to find the tangent value of the angle.
3. The result can be any real number.

Example

Let's calculate tan(45°):

1. Convert 45° to radians: 45° × (π/180°) = π/4 radians
2. Calculate tan(π/4) = 1

Therefore, tan(45°) = 1

Visual Representation

This diagram illustrates tan(45°). The blue line represents the angle of 45°, and the red line shows the tangent value of 1 on the x-axis.