Tangent Calculator Formula

Understand the math behind the tangent calculator. Each variable explained with a worked example.

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Formulas Used

Tangent Val

tangent_val = tan(angle_deg * pi / 180)

Sine Val

sine_val = sin(angle_deg * pi / 180)

Cosine Val

cosine_val = cos(angle_deg * pi / 180)

Variables

VariableDescriptionDefault
angle_degAngle (degrees)(deg)45

How It Works

Tangent Function

Definition

tan(angle) = opposite / adjacent = sin(angle) / cos(angle)

Key Values

Angletan 0°0 30°1/√3 ≈ 0.5774 45°1 60°√3 ≈ 1.7321 90°undefined

Worked Example

Calculate tan(45°).

angle_deg = 45
  1. 01tan(45°) = 1
  2. 02sin(45°) = √2/2 ≈ 0.7071
  3. 03cos(45°) = √2/2 ≈ 0.7071
  4. 04tan = sin/cos = 0.7071/0.7071 = 1

Frequently Asked Questions

What is the tangent function?

Tangent is the ratio of sine to cosine, or equivalently, the ratio of the opposite side to the adjacent side in a right triangle.

Why is tan(90°) undefined?

At 90°, cosine equals zero, and division by zero is undefined. The tangent function approaches infinity as the angle approaches 90°.

What is the period of tangent?

Tangent has a period of 180° (pi radians), which is half the period of sine and cosine.

Learn More

Guide

Trigonometry Basics - Complete Guide

Learn the fundamentals of trigonometry including sine, cosine, tangent, the unit circle, identities, and the laws of sines and cosines with practical examples.

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