Trigonometry Calculator
Inputs
Enter a decimal or expression such as pi/6, π/4, 3π/2, or 45+30.
Result
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Related function values
For angle mode, these values use the same angle. For inverse mode, these show the selected inverse result converted into common angle units.
Unit circle context
Step work
Formulas and assumptions
- Unit conversion: radians = degrees x pi / 180; gradians = degrees x 10 / 9; turns = degrees / 360.
- Core identities: tan(theta) = sin(theta) / cos(theta), cot(theta) = cos(theta) / sin(theta), sec(theta) = 1 / cos(theta), csc(theta) = 1 / sin(theta).
- SOHCAHTOA: sin(theta) = opposite / hypotenuse, cos(theta) = adjacent / hypotenuse, and tan(theta) = opposite / adjacent for a right triangle.
- Inverse ranges: arcsin returns [-90 degrees, 90 degrees], arccos returns [0 degrees, 180 degrees], and arctan returns (-90 degrees, 90 degrees). Arcsec and arccsc use arccos(1/x) and arcsin(1/x). Arccot returns atan(1/x), with arccot(0) = 90 degrees.
- Real-number limits: arcsin and arccos require -1 <= x <= 1. Arcsec and arccsc require |x| >= 1. Values very close to undefined points are treated as undefined to avoid misleading huge rounded numbers.
How to use this calculator
- Choose Angle to value for sin, cos, tan, csc, sec, or cot.
- Choose Value to angle for inverse trig functions such as arcsin or arctan.
- Choose Right triangle when you know two sides and want the angle plus SOHCAHTOA ratios.
- Enter the number or expression, pick a unit and precision, then calculate. Use Copy or Download when you need to reuse the result.
Angles are normalized only for display context; the direct function calculation uses the entered angle after conversion to radians. That preserves values such as tan(450 degrees), which has the same tangent behavior as tan(90 degrees). In radian mode, you can enter pi expressions such as pi/6, π/4, 2*pi/3, and -pi/2.
Common angle values
| Degrees | 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 |
| 180° | π | 0 | -1 | 0 |
| 270° | 3π/2 | -1 | 0 | undefined |
| 360° | 2π | 0 | 1 | 0 |
Common inverse examples
| Expression | Principal value | Radians |
|---|---|---|
| arcsin(0.5) | 30° | π/6 |
| arccos(0.5) | 60° | π/3 |
| arctan(1) | 45° | π/4 |
| arcsec(2) | 60° | π/3 |
| arccsc(2) | 30° | π/6 |
Calculator methodology
Calculations use JavaScript Math trigonometric functions in your browser. Angle inputs are parsed first, converted to radians internally, evaluated at full floating-point precision, and rounded only for display. Undefined reciprocal values use a small tolerance near zero denominators so angles such as 90° return undefined instead of a misleading extremely large rounded number. Exact values are shown when the normalized angle matches a common unit-circle angle within that tolerance.
FAQs
How do I calculate sin, cos, or tan?
Choose Angle to value, select sin, cos, or tan, enter the angle, choose degrees or radians, and calculate. Sine is the unit-circle y-coordinate, cosine is the x-coordinate, and tangent is sine divided by cosine.
Should I use degrees or radians?
Use the unit your problem gives. The calculator accepts degrees, radians, gradians, and turns, then converts the angle to radians internally before evaluating the trig function.
Why does sin(30 degrees) equal 0.5?
On the unit circle, sine is the y-coordinate of the point at the given angle. At 30 degrees, that coordinate is exactly 1/2.
Why does the calculator say tan(90 degrees) is undefined?
Tangent divides sine by cosine. At 90 degrees, cosine is 0, so the division is undefined in real-number arithmetic.
What do csc, sec, and cot mean?
They are reciprocal trig functions: csc(theta) = 1/sin(theta), sec(theta) = 1/cos(theta), and cot(theta) = cos(theta)/sin(theta).
What does inverse trig return?
Inverse trig returns a principal angle. arcsin(x) returns -90° to 90°, arccos(x) returns 0° to 180°, and arctan(x) returns -90° to 90°. The notation sin^-1(x) means arcsin(x), not 1/sin(x).
Can I enter radians with pi?
Yes. Radian mode accepts expressions such as pi/6, π/4, 2*pi/3, 3π/2, and -pi/2. Angle inputs also accept simple arithmetic such as 45+30.
How are negative angles or angles greater than 360 degrees handled?
The calculator evaluates the entered angle and also shows the normalized unit-circle angle from 0° to 360°. For example, -30° and 330° have the same sine, cosine, and tangent values.
Why do exact values differ from decimals?
Exact values such as √2/2 are symbolic forms for special angles. Decimal values are rounded approximations shown at the selected precision.
Does this replace a triangle solver?
No. This calculator evaluates functions for one angle or one inverse input. To solve side and angle combinations, use the Trigonometric Triangle Solver.
Is my calculation private?
Yes. The calculator runs locally in your browser and does not upload or store entered values.