Trigonometric Functions Calculator
All six trigonometric functions of an angle, in degrees or radians, with the inverse of the sine as well.
Sine, cosine and tangent come from the unit circle: for an angle θ measured anticlockwise from the positive x-axis, cos θ is the x coordinate and sin θ the y coordinate.
How the trigonometric functions calculator works
Sine, cosine and tangent come from the unit circle: for an angle θ measured anticlockwise from the positive x-axis, cos θ is the x coordinate and sin θ the y coordinate. Tangent is their ratio, sin/cos, which is why it is undefined wherever cosine is zero — at 90°, 270° and every 180° after.
The other three are reciprocals: cosecant of sine, secant of cosine, cotangent of tangent. Each is undefined wherever the function beneath it is zero, and those points are flagged here rather than returned as a huge number.
Formula: sin²θ + cos²θ = 1; tan θ = sin θ / cos θ
Worked examples
| Inputs | sin θ | Note |
|---|---|---|
| sin 30° | 0.5 | exactly 0.5 |
| cos 60° | 0.8660254038 | 0.5 |
| One radian | 0.8414709848 | sin 0.8415, about 57.3° |
FAQFrequently asked questions
What is sin 30°?
Exactly 0.5 — one of the handful of angles with an exact simple value.
Why is tan 90° undefined?
Because tangent is sine over cosine, and cosine is zero at 90°. The graph has an asymptote there.
What are cosec, sec and cot?
The reciprocals of sine, cosine and tangent. Each is undefined wherever the function beneath it hits zero.
How do I convert degrees to radians?
Multiply by π/180. A full turn is 360° or 2π radians.
Which quadrant is 200°?
The third, where both sine and cosine are negative.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.