Trigonometry Calculator
Evaluate all six trig functions and their inverses in degrees or radians.
About Trigonometry Calculator
Trigonometric functions relate the angles of a right triangle to the ratios of its sides. Sine is opposite over hypotenuse; cosine is adjacent over hypotenuse; tangent is opposite over adjacent. The reciprocal functions (cosecant, secant, cotangent) are 1/sin, 1/cos, 1/tan. The inverse functions reverse the mapping: given a ratio, they return the angle. Angles are expressed in degrees (0–360) or radians (0–2π).
Formulas
Right-triangle definitions
sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj
- opp
- Opposite side
- adj
- Adjacent side
- hyp
- Hypotenuse
Pythagorean identity
sin²θ + cos²θ = 1
Degree ↔ radian conversion
radians = degrees × π/180
Worked example
With the default values below, Trigonometry Calculator returns Result of 0.5000000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Angle modeone of Degrees, Radians
- Degrees
- Functionone of sin(θ), cos(θ), tan(θ), csc(θ) = 1/sin, sec(θ) = 1/cos, cot(θ) = 1/tan, arcsin (sin⁻¹), arccos (cos⁻¹), arctan (tan⁻¹), arccsc (csc⁻¹), arcsec (sec⁻¹), arccot (cot⁻¹)
- sin(θ)
- Angle (θ)
- 30
- Input value
- 0.5
Results
- Result
- 0.5000000000
- Angle (degrees)
- 30.000000 °
- Angle (radians)
- 0.52359878
Step by step
- 1Angle= 30° = 0.52359878 rad
- 2sin(30°)= 0.5
- 3Definition= Opposite / Hypotenuse
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is the difference between degrees and radians?
Both measure angles. Degrees divide a full turn into 360 equal parts. Radians measure the arc length on a unit circle: a full turn is 2π radians ≈ 6.2832. Radians are the natural unit in mathematics and physics because formulas like the derivative of sin(x) = cos(x) only hold when x is in radians.
Why is tan(90°) undefined?
tan(θ) = sin(θ)/cos(θ). At θ = 90°, cos(90°) = 0, so we are dividing by zero. The tangent function has vertical asymptotes at 90°, 270°, and all odd multiples of 90°.
What is the range of arcsin?
The principal value of arcsin returns angles in [−90°, 90°] (or [−π/2, π/2] in radians). This is the conventional 'main branch'. Other angles with the same sine exist but arcsin always returns the one in this range.