Trigonometry Calculator

Calculate sin, cos, tan and inverse trig functions in degrees or radians. Includes a trig table reference for angles. Free online trigonometry calculator for students.

How to Use

  1. Select a function

    Choose sin, cos, tan, or an inverse trigonometric function.

  2. Enter a value

    Input an angle in degrees or radians, or a trigonometric value for inverse functions.

  3. View result

    Click Calculate to see the result displayed in both degrees and radians.

What is trigonometry?

Trigonometric functions express the ratios between two sides of a right triangle as a function of an angle. For a reference angle θ, the three basics are sin (opposite ÷ hypotenuse), cos (adjacent ÷ hypotenuse) and tan (opposite ÷ adjacent), and together with their reciprocals csc, sec, cot there are six functions in all.

Why it matters

Trigonometry goes far beyond solving triangles: it describes every phenomenon that repeats periodically, such as rotation, oscillation and waves. That is why it is used so widely in simple harmonic motion and alternating current in physics, signal processing in engineering, coordinate rotation in computer graphics and slope calculations in architecture.

  • The values at 0°, 30°, 45°, 60° and 90° appear constantly, so it is handy to memorize them.
  • Enter an angle once and this calculator outputs all six function values together with degrees and radians, so you never have to hunt through a table.

Calculation formula

The angle you enter is first converted to radians, then each function value is computed.

radians = degrees × π / 180

sin θ, cos θ, tan θ = sin θ / cos θ

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

Example: entering 30°

radians = 30 × 3.14159 / 180 = 0.5236, sin 30° = 0.5, cos 30° ≈ 0.8660, tan 30° = 0.5 / 0.8660 ≈ 0.5774, csc 30° = 2, sec 30° ≈ 1.1547 and cot 30° ≈ 1.7321.

θ is the reference angle, and where cos θ = 0, such as at 90° and 270°, tan and sec are shown as 'undefined'.

Frequently Asked Questions

What is trigonometry?
Trigonometric functions are defined by the ratios of the sides of a right triangle. sin (sine) is opposite/hypotenuse, cos (cosine) is adjacent/hypotenuse, and tan (tangent) is opposite/adjacent. These three plus their reciprocals csc, sec and cot make up six trigonometric functions in all.
How do I convert between degrees and radians?
To convert degrees to radians, multiply by π/180; to convert radians to degrees, multiply by 180/π. A full turn is 360° = 2π radians, and 1 radian ≈ 57.2958°. For example, 90° = π/2 radians.
What is the relationship between sin, cos and tan?
tan(θ) = sin(θ)/cos(θ), and the Pythagorean identity sin²(θ) + cos²(θ) = 1 always holds. In addition, sin and cos are 90° out of phase, so sin(θ) = cos(90°−θ). Using these relationships, one function value lets you find all the others.
Why is tan 90° undefined?
tan is defined as sin/cos, and at 90° (or 270°) cos becomes 0, which means dividing by zero. In these cases this calculator shows tan and sec as 'undefined'. Likewise, at 0° and 180° where sin is 0, csc and cot are undefined.
What are csc, sec and cot?
They are the reciprocals of sin, cos and tan respectively: csc (cosecant) = 1/sin, sec (secant) = 1/cos and cot (cotangent) = 1/tan. They are not used as often, but they are handy for simplifying expressions in calculus and physics problems.
Can it calculate inverse trig functions (arcsin, etc.)?
Inverse trig functions work backwards from a function value to find the angle. The angle whose sine is 0.5 is found as arcsin(0.5) = 30°. Note, however, that sin and cos only accept inputs between −1 and 1, while tan accepts any real number.
Can I enter negative angles or angles greater than 360°?
Yes. Trigonometric functions are periodic, so sin and cos repeat every 360° (2π) and tan repeats every 180° (π). For example, sin(390°) = sin(30°) = 0.5, and sin(−30°) = −sin(30°) = −0.5, so negative angles are handled naturally.
How precise are the results?
This calculator rounds and displays results to 10 decimal places. It also treats values smaller than 1e−12 as floating-point error and cleans them up to 0, so sin 180° shows exactly 0 rather than 0.0000000001.
Verified 2026 formulas

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