Trigonometry Calculator

Solve trigonometry problems with clear steps, notation, and a final check. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.

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Trigonometry

Trigonometry Calculator explained

The short version

Sine, cosine and tangent are ratios of two sides of a right triangle, so they never carry a unit.
Check DEG or RAD before you press anything. sin 30° = 0.5 but sin 30 radians is about −0.988.
sin⁻¹ means the inverse function, which gives you back an angle. It is not 1 divided by sine.

The formula this page uses

sin θ = opposite / hypotenuse cos θ = adjacent / hypotenuse tan θ = opposite / adjacent sin²θ + cos²θ = 1

What each part means

SymbolWhat it means

θ — The angleMeasured in degrees or radians. Everything downstream depends on which mode is set.

opposite — Opposite sideThe side across the triangle from θ, in any length unit.

adjacent — Adjacent sideThe side touching θ that is not the hypotenuse.

hypotenuse — HypotenuseThe side facing the right angle. Always the longest, so sin θ and cos θ can never exceed 1.

Show your work: a full example

A right triangle with the side opposite θ = 7 and hypotenuse = 25opposite = 7, hypotenuse = 25
Use the sine ratiosin θ = 7 / 25 = 0.28
Take the inverse sine in degree modeθ = sin⁻¹(0.28) = 16.26°
Find the third side with Pythagoras25² − 7² = 625 − 49 = 576
Square-root itadjacent = √576 = 24
Now the cosine ratiocos θ = 24 / 25 = 0.96
Check with the identity0.28² + 0.96² = 0.0784 + 0.9216 = 1

A second, different case

A different case: an obtuse angle, 150°θ = 150°, which lands in the second quadrant
Find the reference angle180° − 150° = 30°
Sine is positive in the second quadrantsin 150° = sin 30° = 0.5
Cosine is negative in the second quadrantcos 150° = −cos 30° = −0.8660
Divide for the tangenttan 150° = 0.5 ÷ (−0.8660) = −0.5774
Convert the angle to radians150 × π/180 = 5π/6 ≈ 2.618
Check with the identity again0.5² + (−0.8660)² = 0.25 + 0.75 = 1

Copy-ready example

opposite = 7, hypotenuse = 25

A right triangle with the side opposite θ = 7 and hypotenuse = 25

Unit circle values worth memorising

Degrees	Radians	sin θ	cos θ	tan θ
0°	0	0	1	0
30°	π/6	1/2	√3/2 ≈ 0.866	√3/3 ≈ 0.577
45°	π/4	√2/2 ≈ 0.707	√2/2 ≈ 0.707	1
60°	π/3	√3/2 ≈ 0.866	1/2	√3 ≈ 1.732
90°	π/2	1	0	undefined
120°	2π/3	√3/2 ≈ 0.866	−1/2	−√3 ≈ −1.732
150°	5π/6	1/2	−√3/2 ≈ −0.866	−√3/3 ≈ −0.577
180°	π	0	−1	0
270°	3π/2	−1	0	undefined

Three mistakes to check for

What students write	Why it's wrong	Do this instead
sin 30 = −0.988	The calculator was in radian mode, so it found the sine of 30 radians instead of 30 degrees.	Switch the mode to DEG and read sin 30° = 0.5.
tan 90° = 0	Tangent divides sine by cosine, and cos 90° = 0, so the division has no answer.	Say tan 90° is undefined, and expect a vertical asymptote there on the graph.
sin⁻¹(0.28) = 1 ÷ sin(0.28)	The −1 marks the inverse function, which converts a ratio back into an angle.	sin⁻¹(0.28) ≈ 16.26°. The reciprocal 1/sin θ is called cosecant.

Questions about the Trigonometry Calculator

How do I tell whether a question wants degrees or radians?

If the angle is written with a degree symbol, or is a familiar number like 30, 45 or 60, it wants degrees. If it contains π, or comes out of a calculus problem, it wants radians. When a problem mixes both, convert everything once at the start.

Why can sin θ never be bigger than 1?

Sine divides a leg by the hypotenuse, and the hypotenuse is always the longest side of a right triangle. A smaller number over a bigger one can never exceed 1, so a calculator answering sin⁻¹(1.4) returns an error rather than an angle.

What does the reference angle actually do for me?

It lets you reuse the values you already know. 150° has a reference angle of 30°, so its sine and cosine have the same size as 30°'s; the quadrant only decides the plus or minus sign.

Which ratio should I pick when I know two sides?

Name the sides relative to the angle you want, then read SOH-CAH-TOA. Opposite and hypotenuse means sine, adjacent and hypotenuse means cosine, opposite and adjacent means tangent. In the worked example 7 and 25 were opposite and hypotenuse, so sine was the only choice.

Where to go next

The scientific calculator has a visible DEG and RAD switch, which is the fastest way to stop the radian-mode error before it happens.
Once the angles become inputs to a graph rather than parts of a triangle, the precalculus calculator handles the period, amplitude and phase shift.
The trigonometry lessons walk the unit circle one quadrant at a time so the sign pattern in the table above stops needing memorisation.

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