Trigonometry Calculator

Last updated: Jul 22, 2026 | Reviewed by Calkulator Team | 2 min read

$Math illustration$

Math

Calculate trigonometric functions and solve triangles

Enter an angle to see all six trig functions (sin, cos, tan, cot, sec, csc) plus their inverses. Switch between degrees and radians. Also solve triangles using the law of sines and cosines when you know sides and angles.

Remember: SOH-CAH-TOA for right triangles, and use the unit circle for angles beyond 90 degrees.

Mode

Angle → Trig Values Triangle Solver

Angle Value

Angle Unit

Key Identities

sin²θ + cos²θ = 1

tan θ = sin θ / cos θ

Law of Sines: a/sin A = b/sin B = c/sin C

Law of Cosines: c² = a² + b² - 2ab²cos C

Area: — � a — b — sin C

Gradians: 400 grad = 360² = 2p rad

Angle

—

In Degrees / Radians / Gradians

—

sin θ

—

cos θ

—

tan θ

—

cot θ

—

sec θ

—

csc θ

—

Inverse Trig (returns angle in degrees)

arcsin(sin θ)

—

arccos(cos θ)

—

arctan(tan θ)

—

Unit Circle

90²

270²

0²

180²

—

Live Result Illustration

Visual summary — updates instantly as you enter values above

LIVE

Real-Life Guide to Using the Trigonometry Calculator

Sin, cos, tan and inverses. Use the examples and checks below to turn the number into a practical decision.

When this calculator is useful

Use this to find the sine, cosine, or tangent of an angle, or to work backward from a ratio to an angle, when solving right-triangle problems in geometry or trigonometry coursework.

For most people, the best way to use the Trigonometry Calculator is to try the real case first, then change one input at a time. That makes the trade-off visible. For example, with a loan calculator you can change tenure while keeping the same rate; with an investment calculator you can change return assumption while keeping the same monthly contribution; with a health, education or measurement calculator you can check how much one input changes the final category.

The result should answer a practical question: Can I afford this? How much should I save? Is this score enough? Is this measurement within range? What is the safer or cheaper option? If the output does not answer the decision clearly, adjust the inputs until the scenario matches your real situation.

Real-Life Example

Finding a right-triangle side: A right triangle has a hypotenuse of 10 cm and a known angle of 30°, and the opposite side length is unknown.

1sin(30°) = opposite ÷ hypotenuse, so opposite = 10 × sin(30°) = 10 × 0.5 = 5 cm.

2Now change one input, such as rate, time, quantity, unit or score, and compare the new result with the first one.

Once you identify which ratio connects a known angle to a known and an unknown side, multiplying or dividing gives the missing length directly.

Practical Advice

Use the Trigonometry Calculator as a planning tool, not just a number generator. Write down the inputs you used, because the final answer is meaningful only when you remember the assumptions behind it.

If the decision affects money, health, tax, safety, academics or legal compliance, keep a second check ready. That second check may be a bank quote, payslip, official rule, prescription, site measurement, mark sheet or invoice.

Common Mistakes

Leaving the calculator in the wrong angle mode, so entering 45 expecting degrees but getting a radian-mode result instead.
Mixing up sine and cosine for the same angle — sine uses opposite over hypotenuse, cosine uses adjacent over hypotenuse, and swapping them gives the wrong ratio.
Forgetting that inverse trig functions (sin⁻¹, cos⁻¹, tan⁻¹) return an angle, not a ratio — sin⁻¹(0.5) should give 30°, not the number 0.5.
Applying SOH-CAH-TOA to a triangle that is not confirmed to have a 90° angle — oblique triangles need the Law of Sines or Law of Cosines instead.
Rounding an intermediate angle or ratio too early in a multi-step problem, which drifts the final side length away from its exact value.

How to Interpret Results

Check whether the number you are reading is a ratio (output of sin, cos, or tan) or an angle in degrees (output of an inverse trig function) — the two look similar but answer completely different questions.

A good interpretation looks at both the main result and the supporting values. If a page shows totals, ratios, categories, schedules or warnings, read those together instead of focusing only on the biggest number.

Trigonometry Calculator FAQs

Useful answers for interpreting the output, avoiding mistakes and using the result responsibly.

What does this calculator compute?

It calculates sine, cosine, and tangent of a given angle, and also works in reverse using inverse functions (arcsin, arccos, arctan) to find an angle from a known ratio.

How do I switch between degrees and radians?

The calculator has a mode toggle, and it is essential to match this to how your problem states the angle — a 45° angle and a 45 radian angle are entirely different positions on the unit circle.

What does SOH-CAH-TOA mean?

It is a memory aid for right-triangle ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent, used to relate a known angle to two of the triangle's three sides.

How is this used in typical right-triangle exam problems?

Problems usually give one angle and one side and ask for another side, or give two sides and ask for an angle — this calculator handles either direction depending on which values you enter.

Why is tan(90°) undefined?

Tangent equals sine divided by cosine, and cosine of 90° is 0, so the division is undefined — this corresponds to a right triangle where the adjacent side would have to be zero.

What happens with angles beyond 90°?

Sine, cosine, and tangent are still defined for angles up to 360° and beyond using the unit circle, but their signs change depending on the quadrant, so a calculator result for a large angle may be negative.

Are there restrictions on inverse trig function results?

Yes — arcsin and arccos only return values in a limited range (typically -90° to 90° for arcsin), so an inverse trig answer will not automatically tell you about other equivalent angles that share the same ratio.

What if my triangle does not have a right angle?

SOH-CAH-TOA does not apply directly to oblique (non-right) triangles — use the Law of Sines or Law of Cosines, which relate all three sides and angles without requiring a 90° angle.

What is a Trigonometry Calculator?

Trigonometry deals with relationships between angles and sides of triangles. The six fundamental functions — sin, cos, tan, csc, sec, cot — are used across physics, engineering, navigation, architecture, and computer graphics. This calculator evaluates all six functions in both degrees and radians.

The triangle solver mode uses the Law of Sines and Law of Cosines to find unknown sides and angles from any valid combination of known values (SSS, SAS, ASA, AAS, SSA) — ideal for geometry problems and real-world triangle calculations.

Example Calculation

Scenario: Arjun, Class 11 JEE aspirant from Kota — needs all 6 trig values at 30² for physics problems involving inclined planes and projectile motion (his Resonance batch test is tomorrow)

1sin(30²) = 0.5 | cos(30²) = 0.866 | tan(30²) = 0.577

2csc(30²) = 2 | sec(30²) = 1.155 | cot(30²) = 1.732

3In radians: 30² = p/6 — 0.5236 rad

✓ All 6 trig functions computed for 30²

How to Use the Trigonometry Calculator

Select the Mode — "Angle → Trig Values" to find all 6 trig functions for a given angle, or "Triangle Solver" to find missing sides and angles of any triangle.
In Angle mode: enter the angle value and select Degrees, Radians, or Gradians — all three formats are supported and converted automatically.
Click "Calculate" — sin, cos, tan, cot, sec, and csc values appear along with inverse trig results; the unit circle visual shows the angle's position.
In Triangle Solver mode: select the known case (SSS, SAS, ASA, AAS, or SSA) and enter the known sides (a, b, c) and/or angles (A, B, C in degrees).
Click "Solve Triangle" — all unknown sides, angles, the triangle area, and perimeter are computed; the triangle type (acute, obtuse, right) is identified.

Benefits

All 6 trig functions (sin, cos, tan, cot, sec, csc) computed simultaneously — no need for separate calculations
Supports Degrees, Radians, and Gradians — converts between all three automatically
Triangle solver handles all 5 congruence cases including the ambiguous SSA case
Visual unit circle shows angle position — helps understand quadrant behavior and sign of functions
Inverse trig values (arcsin, arccos, arctan) shown alongside forward functions for complete reference

Key Terms

Sine (sin θ): Opposite — Hypotenuse in a right triangle; ranges from -1 to 1; reaches maximum (1) at 90²
Cosine (cos θ): Adjacent — Hypotenuse; equals 1 at 0², 0 at 90²; used extensively in dot products and wave equations
Tangent (tan θ): sin θ ÷ cos θ = Opposite — Adjacent; undefined at 90² and 270² where cos = 0
Radian: SI unit of angle: 2p rad = 360²; 1 rad — 57.3². All calculus formulas (derivatives of sin, cos) require radians
Law of Cosines: c² = a² + b² - 2ab²cos C — generalises the Pythagorean theorem; used for SAS and SSS triangle cases

Frequently Asked Questions

When should I use degrees vs radians?

Use degrees for everyday geometry, navigation, and problems that explicitly state angle in degrees — it's more intuitive (full circle = 360²). Use radians for calculus and physics: the derivative of sin(x) = cos(x) is only true when x is in radians. Programming languages like Python's math.sin() and JavaScript's Math.sin() use radians by default. For JEE Physics, most problem statements give angles in degrees, but SHM, wave, and rotational dynamics formulas require radian conversion. This calculator accepts all three units and converts automatically — choose what your problem statement uses.

What is the SSA case and why is it called ambiguous?

SSA (two sides and a non-included angle — the angle doesn't lie between the two known sides) is called the "ambiguous case" because the given information can produce zero, one, or two valid triangles. Given side a, side b, and angle A: if a < b²sin A → no triangle exists; if a = b²sin A → exactly one right triangle; if b²sin A < a < b → two different valid triangles; if a = b → exactly one triangle. This calculator evaluates all conditions and returns the valid solution(s), flagging when two distinct triangles are geometrically possible with the same input data.

What is the Law of Sines and when should I use it?

The Law of Sines states: a/sin A = b/sin B = c/sin C — each side is proportional to the sine of its opposite angle. Use it when you know: (1) two angles and any one side (ASA or AAS) — it finds the remaining sides; (2) two sides and a non-included angle (SSA) — the ambiguous case. It's computationally simple but breaks down for the SAS and SSS cases where you don't have an angle opposite to a known side. The Law of Cosines is required for those cases. Most Class 11²12 and JEE triangle problems use a combination of both laws.

How do I find all angles of a triangle if I only know all three sides (SSS)?

With SSS, use the Law of Cosines: cos A = (b² + c² - a²) / (2bc). Rearrange similarly for angle B using sides a and c. Once you have two angles, the third is simply 180² - A - B (all angles in a triangle sum to 180²). Example with the classic 3-4-5 right triangle: cos A = (16 + 25 - 9) / (2 — 4 — 5) = 32/40 = 0.8 → A = arccos(0.8) — 36.87². Similarly B — 53.13² and C = 90². This calculator performs all these steps automatically — just enter the three sides under the SSS case.

What are the standard trigonometric values I should memorize for exams?

For Class 10²12 boards and JEE: sin 0²=0, sin 30²=�, sin 45²=1/v2²0.707, sin 60²=v3/2²0.866, sin 90²=1. Cos values follow the reverse order: cos 0²=1, cos 30²=v3/2, cos 45²=1/v2, cos 60²=�, cos 90²=0. Tan: 0²=0, 30²=1/v3²0.577, 45²=1, 60²=v3²1.732, 90²=undefined. Memory trick for sin: v0/2, v1/2, v2/2, v3/2, v4/2 (i.e., 0, �, 1/v2, v3/2, 1). For cos, the pattern is reversed. This calculator instantly verifies values for any angle outside these standard ones.