Tangent Angle Calculator
Calculate tangent values from angles or triangle sides with detailed explanations
Calculate Tangent
Enter the angle value
Choose the input unit for your angle
Tangent Results
Calculation: tan(0.00°) = 0.000000
Exact Value: tan(0°) = 0
Period: Tangent has a period of π radians (180°)
Common Tangent Values
Special Angles
tan(0°) = 0
tan(30°) = 1/√3 ≈ 0.577
tan(45°) = 1
tan(60°) = √3 ≈ 1.732
tan(90°) = undefined
Triangle Example
Given: Opposite = 21, Adjacent = 8
Calculation: tan(θ) = 21/8 = 2.625
Angle: θ = arctan(2.625) ≈ 69.1°
Verification: tan(69.1°) ≈ 2.625
Tangent Function Properties
Definition
tan(θ) = opposite/adjacent
Also: tan(θ) = sin(θ)/cos(θ)
Period
π radians (180°)
Repeats every 180°
Asymptotes
At odd multiples of 90°
..., -90°, 90°, 270°, ...
Quadrant Analysis
Quadrant I
0° to 90°
Positive
Quadrant II
90° to 180°
Negative
Quadrant III
180° to 270°
Positive
Quadrant IV
270° to 360°
Negative
Quick Tips
Tangent is the ratio of opposite to adjacent sides
tan(45°) = 1 is a key reference value
Function is undefined at 90°, 270°, etc.
Period is π radians (180°)
Understanding Tangent Function
What is Tangent?
The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. It's one of the fundamental trigonometric functions and can also be expressed as the ratio of sine to cosine: tan(θ) = sin(θ)/cos(θ).
Key Properties
- •Domain: All real numbers except odd multiples of π/2
- •Range: All real numbers (-∞, +∞)
- •Period: π radians (180°)
- •Odd Function: tan(-θ) = -tan(θ)
Practical Applications
- Engineering: Slope calculations and structural analysis
- Physics: Angle of incidence and trajectory calculations
- Navigation: Bearing and heading computations
- Architecture: Roof pitch and ramp angle design
- Surveying: Measuring angles and distances
Asymptotes
Important: The tangent function has vertical asymptotes (undefined values) at angles where cosine equals zero: ..., -90°, 90°, 270°, 450°, ...
Memory Tip: SOH-CAH-TOA helps remember: Tangent = Opposite/Adjacent