Professional Mathematics Tool

Trigonometry Calculator

Calculate sin, cos, tan, inverse trigonometric functions, angles, and right triangle values instantly. Accurate, fast, and free online tool.

Calculation Panel

Result

sin(30°)
0.5

Calculation Steps

  1. Input angle = 30°
  2. Convert angle to radians: 30 × π / 180 = 0.523598
  3. sin(0.523598) = 0.5
  4. Final result = 0.5

History

Unit Circle Visualization

Visual representation of the trigonometric function based on your input (for Basic Functions).

Angle: 30°

sin(θ): 0.500000

cos(θ): 0.866025

tan(θ): 0.577350

Right Triangle Calculator

Enter any two known values (at least one side) to solve the right triangle.

Special Angles Table

Degrees Radians sin cos tan
0°0010
30°π/61/2√3/2√3/3
45°π/4√2/2√2/21
60°π/3√3/21/2√3
90°π/210Undefined
120°2π/3√3/2-1/2-√3
135°3π/4√2/2-√2/2-1
150°5π/61/2-√3/2-√3/3
180°π0-10
270°3π/2-10Undefined
360°2π010

Trigonometric Formulas

Basic Ratios

sin θ = Opposite / Hypotenuse
cos θ = Adjacent / Hypotenuse
tan θ = Opposite / Adjacent

Reciprocal Identities

csc θ = 1 / sin θ
sec θ = 1 / cos θ
cot θ = 1 / tan θ

Pythagorean Identities

sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = csc²θ

What is a Trigonometry Calculator?

A Trigonometry Calculator is an essential online mathematics tool designed to evaluate trigonometric functions instantly. Whether you are dealing with basic functions like sine, cosine, and tangent, or exploring inverse and hyperbolic functions, this tool ensures absolute precision without requiring manual lookups in trigonometric tables.

How to Use the Trigonometry Calculator

Using our tool is straightforward:

  1. Select the desired trigonometric function from the dropdown list.
  2. Enter the angle or value in the input field.
  3. Choose your preferred unit: Degrees, Radians, or Gradians.
  4. Click Calculate to instantly view the result along with step-by-step explanations.

Degrees vs Radians

Angles can be measured in degrees or radians. A full circle is 360 degrees, which is equivalent to 2π radians. This calculator effortlessly converts between these units to evaluate functions based on your specific requirements.

Frequently Asked Questions

It is an advanced digital tool used to compute basic, inverse, and hyperbolic trigonometric functions. It also provides visual aids like unit circles and solves right triangles automatically.

Simply select the function from the dropdown list, input your value, select the appropriate unit (e.g., Degrees), and hit Calculate. The result will appear immediately.

Degrees and radians are two standard units for measuring angles. A full circle is 360 degrees or 2π radians. Use the unit selector to ensure your calculation uses the correct metric.

Yes. It fully supports inverse functions such as asin (arcsin), acos (arccos), and atan (arctan), complete with domain validation to prevent mathematical errors.

Absolutely. Use the Right Triangle Calculator section. Simply input two known values (at least one side length), and the tool will compute the remaining sides and angles using Pythagorean theorem and trigonometric ratios.

For values where the tangent is mathematically undefined (like 90° or 270°), the calculator will explicitly state "Undefined" rather than returning an error or confusing infinite number.