About the Trigonometry Calculator
What is the Trigonometry Calculator?
Trigonometric ratios relate the angles of a right-angled triangle to the lengths of its sides. For an angle θ: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse and tan θ = opposite ÷ adjacent. Their reciprocals are cosec, sec and cot.
Enter any angle — including angles above 90° and negative angles — in degrees or radians. The calculator returns all six ratios using the unit-circle definitions, marks values that are undefined (such as tan 90°) and converts the angle to the other unit.
How to use the Trigonometry Calculator
- Angle (θ) (sample: 30)
- Angle Unit (sample: Degrees)
- Press Calculate Trig Values (results also refresh as you type). The result card shows the sin θ, along with cos θ, tan θ, cosec θ and sec θ.
Formula used
sin θ = opp ÷ hyp, cos θ = adj ÷ hyp, tan θ = sin θ ÷ cos θ
- cosec θ = 1 ÷ sin θ
- sec θ = 1 ÷ cos θ
- cot θ = cos θ ÷ sin θ
- Radians = degrees × π ÷ 180
For angles beyond 90°, the unit circle is used: cos θ and sin θ are the x and y coordinates of the point at angle θ on a circle of radius 1.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Angle (θ) | 30 |
| Angle Unit | Degrees |
| Result | Value |
|---|---|
| sin θ | 0.5 |
| cos θ | 0.866025 |
| tan θ | 0.57735 |
| cosec θ | 2 |
| sec θ | 1.154701 |
| cot θ | 1.732051 |
| Angle in radians | 0.523599 |
Values at standard angles
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | √2/2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | √2/2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | undefined |
Tips for using the Trigonometry Calculator
- Use the identity sin²θ + cos²θ = 1 to check answers.
- Heights and distances: the height of a tree = distance from the tree × tan(angle of elevation).
- Make sure the unit matches your angle — sin 30 in radians is −0.988, not 0.5.