Loading Calculator...
Please wait a moment
Please wait a moment
Calculate the tangent of any angle in degrees or radians. Tangent is the ratio of sine to cosine (tan = sin/cos).
| Degrees | Radians | Exact Value | Decimal |
|---|---|---|---|
| 0° | 0 | 0 | 0.0000 |
| 30° | π/6 | √3/3 | 0.5774 |
| 45° | π/4 | 1 | 1.0000 |
| 60° | π/3 | √3 | 1.7321 |
| 90° | π/2 | undefined | — |
| 120° | 2π/3 | -√3 | -1.7321 |
| 135° | 3π/4 | -1 | -1.0000 |
| 150° | 5π/6 | -√3/3 | -0.5774 |
| 180° | π | 0 | -0.0000 |
| 270° | 3π/2 | undefined | — |
Domain: All θ except 90° + n·180°
Range: All real numbers (-∞, ∞)
Period: π radians (180°)
tan(θ + π) = tan(θ)
Odd function: tan(-θ) = -tan(θ)
Origin symmetry
At θ = 90°, 270°, ...
Where cos(θ) = 0
Because tan = sin/cos, and cos(90°) = cos(270°) = 0. Division by zero is undefined.
Tangent is the length of the line segment from the origin to where the terminal side intersects the line x = 1 (the tangent line to the unit circle).
Tangent is positive in Quadrants I and III (where sin and cos have the same sign), and negative in Quadrants II and IV.