Trigonometry Calculator — Sin, Cos, Tan & Inverse Functions
Calculate all six trigonometric functions (sin, cos, tan, csc, sec, cot) for any angle in degrees or radians. Includes inverse trig functions and a unit circle reference. See also Right Triangle Calculator and Pythagorean Theorem Calculator.
Trigonometric Functions Calculator
Inverse Trigonometric Functions
Enter a value to find the angle. arcsin and arccos accept values between −1 and 1.
How to Use the Trigonometry Calculator
Enter any angle in degrees or radians and click Calculate to see all six trigonometric function values at once. Use the quick angle buttons for common angles like 30°, 45°, 60°, and 90°. The calculator handles all four quadrants and special angles. For inverse calculations, select arcsin, arccos, or arctan, enter a ratio value, and get the corresponding angle in both degrees and radians.
Trigonometric Function Formulas
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent = sin θ / cos θ
csc θ = 1 / sin θ = hypotenuse / opposite
sec θ = 1 / cos θ = hypotenuse / adjacent
cot θ = 1 / tan θ = cos θ / sin θ = adjacent / opposite
Pythagorean identity: sin²θ + cos²θ = 1
Radians to degrees: degrees = radians × (180 / π)
Degrees to radians: radians = degrees × (π / 180)
Example Calculation
Find all trig functions for θ = 45°:
45° = π/4 radians ≈ 0.7854 rad
sin 45° = √2/2 ≈ 0.7071
cos 45° = √2/2 ≈ 0.7071
tan 45° = 1
csc 45° = √2 ≈ 1.4142
sec 45° = √2 ≈ 1.4142
cot 45° = 1
Trigonometric Values Reference Table
| Angle (°) | Radians | sin | cos | tan | csc | sec | cot |
|---|---|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 | undef | 1 | undef |
| 30° | π/6 | 1/2 | √3/2 | √3/3 | 2 | 2√3/3 | √3 |
| 45° | π/4 | √2/2 | √2/2 | 1 | √2 | √2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 | 2√3/3 | 2 | √3/3 |
| 90° | π/2 | 1 | 0 | undef | 1 | undef | 0 |
Frequently Asked Questions
What is the difference between degrees and radians?
Degrees and radians are two units for measuring angles. A full circle is 360° or 2π radians. To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π. Radians are the standard unit in calculus and most mathematical formulas.
Why is tan 90° undefined?
tan θ = sin θ / cos θ. At 90°, cos 90° = 0, so you would be dividing by zero. Geometrically, the tangent line at 90° on the unit circle is vertical and extends to infinity. The same applies to cot 0°, csc 0°, and sec 90°.
What are the reciprocal trig functions?
The three reciprocal functions are cosecant (csc = 1/sin), secant (sec = 1/cos), and cotangent (cot = 1/tan). They are useful in calculus, physics, and engineering for simplifying expressions where division by sin, cos, or tan appears frequently.
What are inverse trig functions used for?
Inverse trig functions (arcsin, arccos, arctan) find the angle when you know the ratio. For example, if sin θ = 0.5, then arcsin(0.5) = 30°. They are essential for solving triangles, navigation, physics problems, and converting between rectangular and polar coordinates.
What is the unit circle?
The unit circle is a circle with radius 1 centered at the origin. For any angle θ, the point on the unit circle is (cos θ, sin θ). It provides a geometric way to understand all trig functions and is the foundation for extending trig beyond right triangles to all real numbers.