Tangent Calculator

How to Calculate or Solve Tangent (tan)

The tangent of an angle is a key concept in trigonometry. It can be calculated by using a right triangle or evaluating a known angle in degrees or radians.

1. Tangent in a Right-Angled Triangle

In a right triangle, the tangent of an angle is the ratio of the length of the side opposite to the angle divided by the length of the adjacent side.

Formula:
tan(θ) = Opposite / Adjacent

Steps:

1. Identify the angle θ.
2. Measure the opposite side to the angle.
3. Measure the adjacent side to the angle.
4. Divide the opposite side by the adjacent side.

Example:

If the opposite side is 4 and the adjacent side is 3:

tan(θ) = 4 / 3 ≈ 1.333

2. Tangent of Known Angles

Some tangent values for standard angles are well-known:

• tan(0°) = 0
• tan(30°) = 1/√3 ≈ 0.577
• tan(45°) = 1
• tan(60°) = √3 ≈ 1.732
• tan(90°) is undefined (vertical line).

3. Degrees and Radians

Angles can be expressed in degrees or radians. The formula to convert degrees to radians is:

Radians = Degrees × (π / 180)

Example: 60° = 60 × (π / 180) = π/3 radians

Key Points:

• Tangent values range from -∞ to +∞.
• tan(45°) = 1, tan(90°) is undefined.
• Tangent is positive in the 1st and 3rd quadrants of the unit circle, negative in the 2nd and 4th quadrants.