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Trigonometry Calculator

Compute sin, cos, tan, csc, sec, cot, inverse, and hyperbolic functions in degrees, radians, or gradians. Unit circle reference and identity card included.

Trigonometry calculator

Choose a mode

All three modes run locally with native browser math; nothing is uploaded.

Given an angle, compute sin, cos, tan, csc, sec, and cot. Pick degrees, radians, or gradians.

Angle unit

A full revolution is 360 degrees. The default in geometry, surveying, and most calculators.

Decimals, fractions like 3/4, and constants like pi or pi/6 are all accepted.

Common angles:

Trigonometric values

theta = 30 deg

In radians: 0.5235987756

sin

sin(theta) = opposite / hypotenuse

0.5

Exact form: 1/2

cos

cos(theta) = adjacent / hypotenuse

0.8660254038

Exact form: sqrt(3)/2

tan

tan(theta) = sin / cos

0.5773502692

Exact form: sqrt(3)/3

csc

csc(theta) = 1 / sin

2

sec

sec(theta) = 1 / cos

1.1547005384

cot

cot(theta) = cos / sin

1.7320508076

Unit circle reference

Exact-form values for the canonical first-revolution angles. Use these to spot-check your answer.

DegreesRadianssincostan
00010
30pi/61/2sqrt(3)/2sqrt(3)/3
45pi/4sqrt(2)/2sqrt(2)/21
60pi/3sqrt(3)/21/2sqrt(3)
90pi/210undefined
1202pi/3sqrt(3)/2-1/2-sqrt(3)
1353pi/4sqrt(2)/2-sqrt(2)/2-1
1505pi/61/2-sqrt(3)/2-sqrt(3)/3
180pi0-10
2703pi/2-10undefined
3602pi010

Reciprocal and quotient identities

  • csc(theta) = 1 / sin(theta), sec(theta) = 1 / cos(theta), cot(theta) = 1 / tan(theta)
  • tan(theta) = sin(theta) / cos(theta), cot(theta) = cos(theta) / sin(theta)

Pythagorean identities

  • sin^2(theta) + cos^2(theta) = 1
  • 1 + tan^2(theta) = sec^2(theta)
  • 1 + cot^2(theta) = csc^2(theta)

Double-angle and half-angle

  • sin(2x) = 2 sin(x) cos(x)
  • cos(2x) = cos^2(x) - sin^2(x) = 2 cos^2(x) - 1 = 1 - 2 sin^2(x)
  • tan(2x) = 2 tan(x) / (1 - tan^2(x))
  • sin^2(x) = (1 - cos(2x)) / 2
  • cos^2(x) = (1 + cos(2x)) / 2

Sum and difference

  • sin(a +/- b) = sin(a) cos(b) +/- cos(a) sin(b)
  • cos(a +/- b) = cos(a) cos(b) -/+ sin(a) sin(b)
  • tan(a +/- b) = (tan(a) +/- tan(b)) / (1 -/+ tan(a) tan(b))

What each function means

  • sin (sine) returns the ratio of the side opposite an angle to the hypotenuse of a right triangle, or equivalently the y-coordinate of the corresponding point on the unit circle.
  • cos (cosine) returns the ratio of the side adjacent to an angle to the hypotenuse, or the x-coordinate on the unit circle.
  • tan (tangent) returns sin / cos, equivalent to opposite / adjacent. tan is undefined at every 90 degrees + k*180 degrees because cos is zero there.
  • csc, sec, cot are the reciprocals of sin, cos, and tan. They share the same undefined points as their reciprocal partner.
  • arcsin, arccos, arctan are the inverse functions. Each one returns the principal-value angle, the standard convention used in calculus and most programming languages.
  • sinh, cosh, tanh are the hyperbolic counterparts, defined via the exponential function. They show up in catenary curves (hanging chains), special relativity, and many integrals.

How to use

  1. Pick a mode: Functions to compute sin, cos, tan, csc, sec, cot from an angle; Inverse to compute arcsin, arccos, arctan, arccsc, arcsec, arccot from a ratio; or Hyperbolic for sinh, cosh, tanh, csch, sech, coth from a real number.
  2. Choose the angle unit. Degrees, radians, and gradians are all supported. The same input field accepts pi, pi/2, pi/3, pi/4, pi/6, fractions like 3/4, and decimal numbers.
  3. Type your angle (Functions mode) or ratio (Inverse mode) or real number (Hyperbolic mode). Tap a Common angle, Common ratio, or Quick value preset to load a textbook example instantly.
  4. Read the six result cards. Each card shows the function expression, the decimal value, and the exact-form value (like sqrt(2)/2) where applicable.
  5. If a value is undefined (for example, tan(90 deg) or csc(0)), the card shows an undefined badge with a short explanation of why.
  6. Use Copy on any single result, or Copy all to grab the entire result block as text. Use Clear to reset the input and try a new value.
  7. Scroll to the unit circle table and identity card for a quick reference of the canonical angles, the Pythagorean identities, the double-angle and half-angle formulas, and the sum-and-difference formulas.

About this tool

Trigonometry Calculator evaluates every common trig function in one tool: the six primary functions (sin, cos, tan, csc, sec, cot), the six inverse functions (arcsin, arccos, arctan, arccsc, arcsec, arccot), and the six hyperbolic functions (sinh, cosh, tanh, csch, sech, coth). Enter an angle and switch between degrees, radians, or gradians at any time; the input accepts decimals, comma-decimals used in European locales, simple fractions like 3/4, and the symbolic constants e and pi so you can type pi/4 or 2pi/3 directly without first converting to a decimal. The Functions mode returns all six trigonometric values at once, with a separate result card for each, an exact-form annotation (1/2, sqrt(2)/2, sqrt(3)/2, and so on) for the canonical unit-circle angles, and an explicit undefined badge with a short explanation wherever a function diverges (tan and sec at 90 degrees + k * 180 degrees, csc and cot at multiples of 180 degrees). The Inverse mode flips the direction: enter a ratio, pick the angle unit you want the answer back in, and read the six inverse values with their domain restrictions enforced (arcsin and arccos only accept -1 to 1; arccsc and arcsec only accept |x| at least 1; arctan and arccot accept any real number). The Hyperbolic mode evaluates the exponential-defined siblings sinh, cosh, tanh, csch, sech, coth, which show up in catenary curves, special relativity, and many integrals. The unit-circle reference table shows the standard angles in degrees and radians along with their exact sin, cos, and tan values, the identity card lists the reciprocal, quotient, Pythagorean, double-angle, half-angle, and sum-and-difference formulas, and the result panel surfaces both the decimal answer and a copy-friendly text block for pasting into homework, notes, lab reports, or code. Computation runs entirely in your browser using native Math primitives; the values you enter here never leave your device.

Free to use. Works in your browser. No signup, no login.

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