Trigonometry Calculator
Find all six trigonometric functions of an angle in degrees or radians, with exact values at multiples of 15°.
Change the values and press Calculate to work out your own figures.
Enter an angle and choose degrees or radians.
| Function | Value | Exact |
|---|---|---|
| sin(θ) | 0.5 | 1/2 |
| cos(θ) | 0.8660254038 | √3/2 |
| tan(θ) | 0.5773502692 | √3/3 |
| csc(θ) | 2 | 2 |
| sec(θ) | 1.154700538 | 2√3/3 |
| cot(θ) | 1.732050808 | √3 |
Show the working
- θ = 30° = 0.5235987756 rad = π/6
- tan = sin ÷ cos; csc = 1 ÷ sin; sec = 1 ÷ cos; cot = cos ÷ sin
How to use it
Enter an angle and choose degrees or radians.
Enter the values you know (decimals, fractions, surds such as 2√5, or angles such as π/3 in radians). Show the working gives the rule used at each step.
Key facts
tan = sin ÷ cos; csc = 1 ÷ sin; sec = 1 ÷ cos; cot = 1 ÷ tan
Undefined values
tan and sec are undefined where cos θ = 0 (90°, 270°); cot and csc where sin θ = 0 (0°, 180°).
Questions
What are the functions of 30°?
sin 1/2, cos √3/2, tan √3/3, csc 2, sec 2√3/3, cot √3.
Radians?
Choose radians; π/6 is 30°.
Formulas
tan = sin ÷ cos; csc = 1 ÷ sin; sec = 1 ÷ cos; cot = 1 ÷ tan
Sources
Limitations
- Angles can be typed in degrees or radians; radians may be written with π (π/3, 2pi/3).