Trigonometry Calculator

Calculate sin, cos, tan, and inverse trig functions.

Calculators

How to Use Trigonometry Calculator

  1. 1Enter an angle value
  2. 2Select degrees, radians, or gradians
  3. 3See all trigonometric function values instantly
  4. 4Switch to Inverse mode to use arcsin/arccos/arctan

About Trigonometry Calculator

The Trigonometry Calculator computes all six trigonometric functions for any angle: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Enter an angle in degrees, radians, or gradians and see all six values instantly.

The calculator also includes an inverse mode for arcsin, arccos, and arctan — the functions that return the angle when you know the ratio. Results are shown in all three angle units simultaneously so you can work in your preferred system and cross-reference with others.

All processing runs in your browser with no server calls, delivering instant results for physics, engineering, navigation, and math coursework. Special cases like tan(90°) are handled correctly with clear notations.

Key Features of Trigonometry Calculator

  • Compute all six trig functions: sin, cos, tan, csc, sec, cot
  • Toggle between degrees, radians, and gradians angle modes
  • Inverse mode for arcsin, arccos, and arctan
  • Shows results for all angle units simultaneously
  • Handles special values: tan(90°) = undefined, cot(0°) = undefined
  • High-precision floating-point results
  • Instant results as you type
  • Fully browser-based with no server dependency

Examples

All six functions for 45 degrees

Calculate all trig functions for a 45-degree angle.

Input

45 degrees

Output

sin: 0.7071 | cos: 0.7071 | tan: 1 | csc: 1.4142 | sec: 1.4142 | cot: 1

Inverse trig: find angle from sine

Find the angle whose sine is 0.5 (should give 30 degrees).

Input

arcsin(0.5)

Output

30 degrees | 0.5236 radians | 33.33 gradians

Common Use Cases

  • Evaluating trig function values for physics and engineering problems
  • Finding angles from ratios using inverse trig functions
  • Checking trig identities by computing both sides
  • Navigation and surveying calculations using bearing angles
  • Computing wave function values in signal processing
  • Verifying trig homework and test answers

Troubleshooting

Using the wrong angle mode (degrees vs radians)

Solution

sin(30) in degrees = 0.5, but sin(30) in radians ≈ -0.988. Always confirm the angle mode matches your input. Most textbook problems specify the unit.

Expecting tan(90°) to return a number

Solution

tan(90°) is mathematically undefined because cos(90°) = 0, causing division by zero. The calculator shows "undefined" for these special angles.

Entering a value outside the valid range for arcsin or arccos

Solution

arcsin and arccos are only defined for inputs between -1 and 1 (inclusive). Entering values outside this range produces no real result.

Frequently Asked Questions

Which angle units are supported?

Degrees (0-360), radians (0 to 2pi), and gradians (0-400). Most everyday and classroom calculations use degrees. Radians are standard in higher mathematics and calculus.

What are the six trigonometric functions?

sin (opposite/hypotenuse), cos (adjacent/hypotenuse), tan (opposite/adjacent), csc = 1/sin, sec = 1/cos, and cot = 1/tan. Csc, sec, and cot are the reciprocals of the primary three.

What is a gradian?

A gradian (also called gon) divides a full circle into 400 equal parts instead of 360 degrees. 1 right angle = 100 gradians = 90 degrees. Gradians are used in some surveying and geodesy applications.

Why is tan(90°) undefined?

tan(theta) = sin(theta) / cos(theta). At 90 degrees, cos(90) = 0, so the division is undefined. The tangent function has vertical asymptotes at 90 and 270 degrees.

How do I use inverse trig functions?

Switch to Inverse mode and enter a ratio value between -1 and 1 (for arcsin and arccos) or any real number (for arctan). The result is the angle in your selected unit.

What is the range of arcsin and arccos?

arcsin returns angles from -90 to 90 degrees (-pi/2 to pi/2 radians). arccos returns angles from 0 to 180 degrees (0 to pi radians). These are the principal value ranges.

Can I compute trig for very large angles?

Yes. For angles larger than 360 degrees, the calculator uses the periodicity of trig functions to return the equivalent value in the principal range.

Is my data private?

Yes. All calculations run entirely in your browser. No values are transmitted to any server.