🎓 Mathematics • Trigonometry
100% Client-Side Privacy
Tangent Calculator
Computes tangent for angles in degrees and radians, calculating slope and detecting asymptotes.
Unit Circle Angles:
Trigonometric Functions & Unit Circle Calculator
Angle = 45° = 0.7854 rad (≈ 0.25π)
Trigonometric Ratios & Unit Circle Coordinates
(cos θ, sin θ) = (0.7071, 0.7071)
Sinesin(θ) = 0.7071Exact: √2/2
Cosinecos(θ) = 0.7071Exact: √2/2
Tangenttan(θ) = 1Exact: 1
Cosecant (1/sin)csc(θ) = 1.4142
Secant (1/cos)sec(θ) = 1.4142
Cotangent (1/tan)cot(θ) = 1
What is the Tangent Function?
The tangent represents the ratio of sine to cosine, or opposite side to adjacent side in a right triangle.
Formula & Step-by-Step Calculation
tan(θ) = sin(θ) / cos(θ) = Opp / Adj
Represents the geometric slope of the ray at angle θ.
Worked Step-by-Step Examples
Example 1
tan(45°)
Solution: 1
• sin(45°) / cos(45°) = (√2/2) / (√2/2) = 1
Common Real-World & Academic Use Cases
- ✓ Roof pitch and roadway gradients
- ✓ Shadow length height calculations
- ✓ Optics reflection angles
How to Use the Tangent Calculator
1
Enter Angle
Input angle value.
2
View Tangent
Read tangent value or asymptote status.
Frequently Asked Questions
Q: Why is tan(90°) undefined?
Because cos(90°) = 0, dividing by zero produces a vertical asymptote.