Trigonometry Calculator

How to Use the Trigonometry Calculator

Choose degrees or radians

Pick the unit your angle is in. Degrees are the everyday choice; radians are standard in calculus and physics.

Enter an angle

Type the angle and the calculator shows all six trigonometric functions — sine, cosine, tangent, and their reciprocals cosecant, secant, and cotangent — at once.

See exact common values

For the standard angles like 30°, 45°, 60°, and 90°, the calculator gives exact values — sin 30° is exactly 0.5, not 0.4999999.

Work backwards

Use the inverse section to go the other way: enter a value and find the angle whose sine, cosine, or tangent it is.

Trigonometry, Made Concrete

Angles and Ratios

Trigonometry connects the angles of a triangle to the ratios of its sides, and the three core functions — sine, cosine, and tangent — are simply those ratios. In a right triangle, the sine of an angle is the opposite side over the hypotenuse, the cosine is the adjacent over the hypotenuse, and the tangent is the opposite over the adjacent. From those three come three more, their reciprocals: cosecant, secant, and cotangent. This calculator shows all six at once for any angle, so you never have to remember which is the reciprocal of which. It works in both degrees and radians — degrees for everyday geometry and surveying, radians for calculus and physics where they make the formulas cleaner — and it switches between them with one tap. Crucially, it returns exact values for the special angles: sin 30° is shown as 0.5, not 0.4999999, and sin 180° is exactly 0, avoiding the tiny floating-point errors that make a calculator look unprofessional.

Although trigonometry is taught with right triangles, its real power is that it describes anything that repeats. Wrap an angle around a circle and the sine and cosine trace out smooth waves — and those waves are the mathematics of sound, light, alternating current, springs, tides, and orbits. Every oscillation, every signal, every cycle in nature and engineering is built from sines and cosines, which is why trigonometry sits at the heart of physics, electronics, music, and computer graphics. The inverse functions — arcsine, arccosine, arctangent — run the relationship backwards: given a ratio, they find the angle that produces it, which is exactly what you need to work out an angle of elevation, the direction of a vector, or the phase of a wave. This calculator includes those too, with the same degree/radian choice, so you can move freely in both directions.

"Sine and cosine are the mathematics of everything that repeats — sound, light, tides, orbits. A right triangle is just where they are easiest to see."

Why Exact Values Matter

A subtle but real mark of quality in a trig calculator is how it treats the special angles. Because computers store numbers in binary, a naive calculation of sin 180° gives something like 0.00000000000000012 instead of 0, and cos 90° comes out slightly off zero — tiny errors, but visible and confidence-eroding. This calculator recognises the standard angles and their exact values (the multiples of 30° and 45°) and returns the clean answer, while still giving full high-precision results for every other angle. That blend — exact where exactness exists, high precision everywhere else — is what you want whether you are checking homework, where the textbook answer is the clean fraction, or doing engineering, where the precision matters. Everything runs in your browser, instantly and privately, with the same trusted trig engine that powers the triangle and scientific calculators across the site.

10 Facts About Trigonometry

01

Sine = opposite ÷ hypotenuse; cosine = adjacent ÷ hypotenuse.

02

Tangent = sine ÷ cosine = opposite ÷ adjacent.

03

Cosecant, secant, and cotangent are the reciprocals of the first three.

04

sin 30° is exactly 0.5; this tool shows it exactly, not 0.4999999.

05

tan 90° is undefined — cosine is zero there.

06

A full circle is 360° or 2π radians.

07

Sine and cosine trace waves — the maths of sound and light.

08

The inverse functions find an angle from a ratio.

09

The word "sine" comes from a mistranslation of an Arabic term.

10

Trigonometry underpins GPS, music, and computer graphics.

Frequently Asked Questions

Choose degrees or radians, then enter your angle. The calculator instantly shows sine, cosine, tangent, and their reciprocals cosecant, secant, and cotangent — all six functions at once, so you do not have to compute the reciprocals separately.
They are two units for measuring angles. A full circle is 360 degrees or 2π radians, so 180° equals π radians. Degrees are common in geometry, surveying, and everyday use; radians are standard in calculus and physics because they make the formulas simpler. Toggle the unit and the calculator interprets your angle accordingly.
Because the calculator recognises the special angles and returns their exact values. A naive computation would give a tiny floating-point error like 0.00000000000000012; this tool snaps such results to the clean value, so sin 180° is 0 and sin 30° is exactly 0.5, while still giving full precision for other angles.
Tangent is sine divided by cosine, and at 90° the cosine is zero, so you would be dividing by zero — which is undefined. The calculator says "undefined" rather than returning a huge misleading number, which is the mathematically honest answer.
They run the relationship backwards: given a ratio, they find the angle that produces it. Arcsine of 0.5 is 30°, for instance. Use the inverse section to work out an angle of elevation, the direction of a vector, or any angle when you know the side ratio. Arcsine and arccosine need a value between −1 and 1; arctangent accepts any value.
They are the reciprocals of the three main functions: cosecant is 1 over sine, secant is 1 over cosine, and cotangent is 1 over tangent. They appear often in calculus and physics. The calculator shows all six together so you never have to flip the fractions yourself.
Yes. Because the trig functions are periodic, an angle of 390° gives the same values as 30°, and negative angles are handled correctly too. Enter any value and the calculator returns the right result.
When you plot sine or cosine against a growing angle, you get a smooth repeating wave — and those waves model anything periodic: sound, light, alternating current, springs, tides, and orbits. This is why trigonometry is central to physics, electronics, music, and computer graphics, far beyond its triangle origins.
Yes. Everything is computed in your browser — nothing is uploaded, stored, or logged — and it works offline once loaded.
Completely free, with no account, sign-up, or limit. It runs entirely in your browser and collects no data. Use it as often as you like.

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