Angle Calculator Form
Use angle mode for direct trig values, inverse mode for finding a principal angle, or side mode for right triangle physics and geometry work.
Formula Used
Right Triangle Ratios
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent = sin θ / cos θ
Inverse Functions
θ = sin⁻¹(ratio)
θ = cos⁻¹(ratio)
θ = tan⁻¹(ratio)
Angle Conversion
Radians = Degrees × π / 180
Degrees = Radians × 180 / π
Right Triangle Side Check
h² = opposite² + adjacent²
How to Use This Calculator
1. Choose the calculation type
Select direct angle mode, inverse ratio mode, or right triangle side mode based on the information you already have.
2. Enter your known values
Provide the angle, the trig ratio, or at least two triangle sides. Then choose a precision for your output.
3. Press calculate
The page shows the result above the form, including angle values, sin, cos, tan, notes, and the main formula used.
4. Review the graph and export
Inspect the Plotly graph, compare values, and save your work with the CSV or PDF export buttons.
Example Data Table
| Angle (Degrees) | Angle (Radians) | sin θ | cos θ | tan θ |
|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 |
| 30 | π/6 | 0.5 | 0.866025 | 0.577350 |
| 45 | π/4 | 0.707107 | 0.707107 | 1 |
| 60 | π/3 | 0.866025 | 0.5 | 1.732051 |
| 90 | π/2 | 1 | 0 | Undefined |
Frequently Asked Questions
1. What do sine, cosine, and tangent represent?
They describe angle relationships in a right triangle. Sine compares opposite to hypotenuse, cosine compares adjacent to hypotenuse, and tangent compares opposite to adjacent.
2. Should I use degrees or radians?
Use degrees for classroom problems, drawings, and common angle references. Use radians for calculus, wave motion, rotation formulas, and many physics equations.
3. Why can tangent become undefined?
Tangent equals sin θ divided by cos θ. When cosine becomes zero, the denominator vanishes, so tangent is undefined at those angles.
4. Can this calculator handle negative angles?
Yes. Negative angles work in direct angle mode. The graph marks a coterminal version between -180° and 180° for easier viewing.
5. Why do inverse sine and inverse cosine need values from -1 to 1?
Sine and cosine never exceed 1 or go below -1 for real angles. Inputs outside that range do not produce real angle results.
6. Does inverse trig return every possible angle?
No. The calculator returns the principal angle. It also shows the general solution note so you can build the complete angle family.
7. What happens in the side-based method?
The calculator uses two or three right triangle sides, checks consistency, estimates a missing side when possible, and then finds the angle and trig ratios.
8. Why is the graph useful for physics work?
It helps you see periodic behavior, compare functions visually, and confirm whether your computed angle matches expected trigonometric patterns.