Tan Calculator
Calculate the tangent of any angle in degrees or radians, with pole detection.
Inputs
tan(θ)
1.0000000000
Angle (degrees)
45.000000°
Angle (radians)
0.78539816
Step by step
Convert to radians
45 degrees = 0.78539816 rad
Check for poles
= No singularity detected
Apply tan function
tan(0.78539816)
= 1
How it works
The tangent function returns the ratio of the opposite side to the adjacent side (equivalently sin/cos). It is undefined at 90° + k·180° where cos = 0. This calculator detects those poles and returns a descriptive message rather than an error value.
Formula
Tangent definition
tan θ = sin θ / cos θ = opposite / adjacent
- θ
- The angle
- opposite
- Side opposite to θ
- adjacent
- Side adjacent to θ
Frequently Asked Questions
Why is tan(90°) undefined?
tan(θ) = sin(θ)/cos(θ). At 90°, cos = 0, so we divide by zero. The function has vertical asymptotes at all odd multiples of 90°.
What is tan(45°)?
tan(45°) = 1, because sin(45°) = cos(45°) ≈ 0.7071, and their ratio is exactly 1.