Calculator inputs
Formula used
tan(θ) = sin(θ) / cos(θ), csc(θ) = 1 / sin(θ), sec(θ) = 1 / cos(θ), and cot(θ) = cos(θ) / sin(θ).
Radians = Degrees × π / 180. Degrees = Radians × 180 / π.
Inverse functions return angles. Hyperbolic functions use exponential definitions.
How to use this calculator
- Select a calculation mode and trigonometric function.
- Enter an angle, value, expression, batch, or range.
- Choose the angle unit, precision, notation, and rounding mode.
- Enable exact values, steps, graphing, or all-function output.
- Press calculate, then copy or export the result.
Special-angle reference table
| Angle | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | √3/3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | Undefined |
Example calculations
| Function | Input | Unit | Expected approximation |
|---|---|---|---|
| sin | 30 | Degrees | 0.5 |
| cos | pi/4 | Radians | 0.70710678 |
| tan | 60 | Degrees | 1.73205081 |
| asin | 0.5 | Degrees output | 30 |
| sinh | 1 | Numeric input | 1.17520119 |
Important notes
Tangent and secant are undefined when cosine equals zero. Cotangent and cosecant are undefined when sine equals zero. Near those points, tiny input changes can create large output changes.
Inverse sine and inverse cosine require inputs between negative one and one. Inverse secant and inverse cosecant require absolute inputs of at least one. Inverse hyperbolic functions also have real-number domain limits.
Decimal results use floating-point arithmetic. Exact forms appear only for recognized special angles. Exported values follow the selected precision settings.
Frequently asked questions
What is a decimal approximation?
It is a rounded numerical form of a trigonometric value. The exact value may contain radicals or fractions. Precision controls the displayed decimal length.
Should I choose degrees or radians?
Choose the unit used by your problem. Calculus usually uses radians. Geometry exercises often use degrees.
Can I enter π?
Yes, enter pi or the π symbol. Expressions like pi/6 are supported. Automatic detection can treat them as radians.
Why is tangent sometimes undefined?
Tangent divides sine by cosine. Division fails when cosine equals zero. The calculator reports that condition clearly.
What does significant figures mean?
Significant figures count meaningful digits from the first nonzero digit. They differ from fixed decimal places. Set zero to disable them.
Can the calculator process many angles?
Yes, use batch or range mode. Batch mode accepts comma-separated expressions. Range mode creates evenly spaced values.
Are inverse functions supported?
Yes, arcsine, arccosine, arctangent, arcsecant, arccosecant, and arccotangent are included. Their outputs use your chosen unit. Domain checks prevent invalid real results.
Can I verify an identity?
Yes, identity mode compares both sides numerically. It reports the residual difference. Very small residuals indicate agreement.
How accurate are the results?
Results use the server’s floating-point mathematics. Most ordinary inputs are highly accurate. Near asymptotes, numerical sensitivity increases.