About the Trigonometry Calculator
This trigonometry calculator evaluates the six trig functions — sine, cosine, tangent, cosecant, secant and cotangent — and the inverse functions arcsin, arccos and arctan. Choose a function, type the angle (or the ratio, for an inverse), pick degrees or radians, and you get the answer plus all six ratios for that angle and the angle in both units.
It is meant for students working through right-triangle and unit-circle problems, and for anyone who needs a quick trig value for a physics, engineering, surveying or construction calculation without hunting for the DEG/RAD switch on a handheld calculator.
Values that are mathematically undefined, such as tan 90° or csc 0°, are reported as “Undefined” instead of a huge rounding artefact. Inverse functions return the principal value: arcsin and arctan between −90° and 90°, arccos between 0° and 180°.
With the default inputs, the result is 0.5. Change any value above to recalculate instantly.
How to use the trigonometry calculator
- 1Choose the trig function or its inverse.
- 2Enter the angle — or, for arcsin/arccos/arctan, the ratio.
- 3Choose degrees or radians.
- 4Read the result and the full set of six ratios for the angle.
Formula and method
In a right triangle the three primary ratios compare the sides relative to angle θ: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. On the unit circle, cos θ and sin θ are the x and y coordinates of the point at angle θ, which extends the definitions to any angle, including negative ones and those over 90°.
The reciprocal functions are csc = 1/sin, sec = 1/cos and cot = cos/sin; they are undefined whenever the denominator is zero. Inverse functions work backwards from a ratio to an angle and return the principal value. Degrees convert to radians by multiplying by π/180.
- θ
- The angle, in degrees or radians
- opp, adj, hyp
- Opposite side, adjacent side and hypotenuse of a right triangle
- x
- The ratio passed to an inverse function
Worked examples
sin 30°
sin 30° is exactly 0.5 — the side opposite 30° is half the hypotenuse. cos 30° = √3/2 ≈ 0.866 and tan 30° ≈ 0.577. In radians, 30° is π/6 ≈ 0.5236.
tan of 1 radian
One radian is about 57.30°. tan 1 ≈ 1.5574, and its reciprocal cot 1 ≈ 0.6421.
arcsin 0.5 in degrees
The angle whose sine is 0.5 is 30° (π/6 rad). arcsin returns the principal value between −90° and 90°.
arctan 1 in radians
A tangent of 1 means opposite equals adjacent, which happens at 45°, or π/4 ≈ 0.7854 radians.
Frequently asked questions
How do I remember sin, cos and tan?+
SOH-CAH-TOA: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent, all measured relative to the angle you are working with.
Should I use degrees or radians?+
Use whatever your problem uses. Everyday geometry and surveying use degrees; calculus, physics and most programming languages use radians. 180° equals π radians.
Why is tan 90° undefined?+
tan θ = sin θ ÷ cos θ, and cos 90° is exactly 0, so the division is impossible. As θ approaches 90° the tangent grows without limit.
What is the difference between sin⁻¹ and csc?+
sin⁻¹ (arcsin) is the inverse function: it takes a ratio and returns an angle. csc is the reciprocal: csc θ = 1 ÷ sin θ, which is a ratio, not an angle.
Why does arcsin only accept values between −1 and 1?+
Sine is a ratio of a side to the hypotenuse, which is always the longest side, so sin θ can never exceed 1 or fall below −1. No real angle has a sine of 2.