Looking for a fast, accurate trigonometry calculator? Use this free trig calculator to evaluate sin, cos, tan (and sec, csc, cot) in degrees or radians, solve trigonometric equations, work out right-triangle sides and angles, convert degrees ↔ radians, and browse a handy trigonometry table with key identities and inverse trigonometry formulas. Ideal for GCSE, A-level, university maths, engineering, and physics.
Choose Degrees or Radians.
Enter an angle (e.g., 45, π/4, 3*pi/2).
Select a function: sin, cos, tan, sec, csc, cot (or view all).
Click Calculate to see precise values.
Use Inverse, Solve Eq, Right Triangle, Convert, or Table tabs for more tools.
Tip: You can type pi or π in inputs. The calculator accepts simple expressions like
pi/6,2*pi/3, or45+30.
sin(x)=k, cos(x)=k, tan(x)=kEvaluate sin(θ), cos(θ), and tan(θ) instantly in degrees or radians. The tool also returns sec(θ) = 1/cos(θ), csc(θ) = 1/sin(θ), and cot(θ) = 1/tan(θ) (where defined).
Examples
sin(30°) = 0.5
cos(60°) = 0.5
tan(45°) = 1
sin(π/6) = 0.5, cos(π/3) = 0.5, tan(π/4) = 1
Solve equations of the form sin(x) = k, cos(x) = k, and tan(x) = k. The solver provides the principal solution and the general solution pattern, plus all solutions in a standard range ([0°, 360°] or [0, 2π]).
Examples
sin(x) = 1/2 → x = 30°, 150° + 360°·n
cos(x) = √3/2 → x = ±30° + 360°·n
tan(x) = 1 → x = 45° + 180°·n
Find angles from a given ratio using arcsin, arccos, and arctan. The calculator respects each function’s principal range:
arcsin(y) → range: [−90°, 90°] or [−π/2, π/2]
arccos(y) → range: [0°, 180°] or [0, π]
arctan(y) → range: (−90°, 90°) or (−π/2, π/2)
Given any two valid values (with at least one side), the right-triangle calculator (with C = 90°) computes missing sides and angles using Pythagoras and SOH-CAH-TOA:
If you know a & b → c = √(a² + b²); angles from tan⁻¹.
If you know c & A → a = c·sin A, b = c·cos A.
If you know a & A → b = a / tan A, c = a / sin A.
Convert degrees to radians and radians to degrees:
rad = deg × π / 180
deg = rad × 180 / π
Examples
180° = π rad
π/3 rad = 60°
0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360°
sin²x + cos²x = 1
1 + tan²x = sec²x
1 + cot²x = csc²x
sin(A ± B) = sinA·cosB ± cosA·sinB
cos(A ± B) = cosA·cosB ∓ sinA·cosB
tan(A ± B) = (tanA ± tanB) / (1 ∓ tanA·tanB)
x = arcsin(y), x = arccos(y), x = arctan(y) with domain/range notes
Reference angles, quadrant signs, and periodicity for sin, cos, tan
Enter an angle (in degrees or radians) and select sin, cos, or tan. The calculator instantly returns accurate values, plus sec, csc, cot if you choose “All”.
Yes. Use Solve Eq. Enter k (e.g., 0.5 or sqrt(3)/2) and choose a range ([0°, 360°] or [0, 2π]). You’ll get the principal and general solutions.
arcsin, arccos, and arctan return angles from ratios. The calculator enforces the correct principal ranges so results align with standard definitions.
Yes—as long as at least one is a side and the inputs form a valid right triangle (C = 90°). It uses Pythagoras and SOH-CAH-TOA to fill the rest.
When denominators approach zero (e.g., cos(90°) = 0), sec becomes undefined (∞). The tool will indicate where values are not defined.