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.

Tangent Calculator

Calculate the tangent of an angle in degrees. Shows sine, cosine, and tangent together.

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Angle (degrees)

deg

Tangent Val

1.00000000

Sine Val0.70710678

Cosine Val0.70710678

View formula & 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

Example Calculation

Calculate tan(45°).

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

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