Trigonometry calculator
sin, cos, tan and their inverses in degrees or radians, with exact values for special angles.
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sin 30°
1/2
≈ 0.5
- cos 30°
- √3/2 ≈ 0.866025403784
- tan 30°
- √3/3 ≈ 0.57735026919
- In radians
- π/6 ≈ 0.523598775598
This is an example. Enter your numbers above and press the button to see your own result.
All six functions (30°)
| sin 30° | 1/2 ≈ 0.5 |
|---|---|
| cos 30° | √3/2 ≈ 0.866025403784 |
| tan 30° | √3/3 ≈ 0.57735026919 |
| csc 30° | 2 |
| sec 30° | 2√3/3 ≈ 1.15470053838 |
| cot 30° | √3 ≈ 1.73205080757 |
Show the math
| Position | Quadrant I, reference angle 30° |
|---|---|
| Signs | sin positive, cos positive |
| Other functions | tan = sin/cos, csc = 1/sin, sec = 1/cos, cot = cos/sin |
What to do next
How it works
For angles that are multiples of 15°, the calculator finds the reference angle and quadrant and gives the exact value with its sign, so sin 210° is -1/2. Other angles are computed in radians and rounded to 12 significant digits.
tan, csc, sec and cot come from sin and cos: tan = sin/cos, csc = 1/sin, sec = 1/cos and cot = cos/sin.
Things to keep in mind
Check the unit. sin(30) in radians is about -0.988, not 0.5. Most homework problems in degrees need the Degrees setting.
Sources
- NIST DLMF 4.14, Trigonometric functions: definitions and periodicityChecked 2026-10-19
- NIST DLMF 4.23, Inverse trigonometric functionsChecked 2026-10-19
Frequently asked questions
What is sin 30°?
Exactly 1/2. cos 30° is √3/2 (about 0.866) and tan 30° is √3/3 (about 0.577).
How do you convert degrees to radians?
Multiply by π/180. 120° × π/180 = 2π/3, about 2.094 radians. To go back, multiply by 180/π.
Why is tan 90° undefined?
tan is sin divided by cos, and cos 90° is 0. Dividing by zero has no value, so tan 90° and sec 90° are undefined.
Why does sin⁻¹(0.5) give only 30° when 150° also works?
Inverse functions return one principal value. sin⁻¹ answers between -90° and 90°, so you get 30°. The table under the result lists 150° too.