Trigonometric functions relate angles to ratios of sides in right triangles and to points on the unit circle.
How to use the Trigonometric Functions Calculator
- Angle
Results update as you type, and every field accepts the units shown in its menu.
How it works
The angle is converted to radians internally and each function is evaluated.
What each result means
- sin = sin(rad([Angle]))
- cos = cos(rad([Angle]))
- tan = tan(rad([Angle]))
- csc = 1÷sin(rad([Angle]))
- sec = 1÷cos(rad([Angle]))
- cot = 1÷tan(rad([Angle]))
Example values
How the main result changes when Angle changes and everything else stays at the example values above:
| Angle (°) | sin |
|---|---|
| 15 | 0.2588 |
| 22.5 | 0.3827 |
| 30 | 0.5 |
| 37.5 | 0.6088 |
| 45 | 0.7071 |
| 60 | 0.866 |
Formula
sin θ, cos θ, tan θ = sin θ ÷ cos θcsc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θWorked example
Inputs — Angle: 30 °.
Results — sin = 0.5; cos = 0.8660254; tan = 0.57735027; csc = 2; sec = 1.15470054; cot = 1.73205081; Reference angle = 30 °.
Key terms
- Unit circle
- A circle of radius 1 used to define trig functions for all angles.
Frequently asked questions
Why is tan 90° undefined?
cos 90° is zero, and division by zero is undefined.
How do I remember the ratios?
SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
What formula does the Trigonometric Functions Calculator use?
sin θ, cos θ, tan θ = sin θ ÷ cos θ.