Trigonometry Calculator
Calculate sin, cos, tan and all trigonometric functions for any angle. Solve right triangles with sides and angles instantly.
Enter any angle value (positive or negative)
Trigonometric Values
How to Use the Trigonometry Calculator
- Choose between Trig Functions mode to calculate sin, cos, tan for an angle, or Right Triangle mode to solve a triangle from known sides or angles.
- Select whether you want to enter your angle in degrees or radians using the toggle buttons.
- Type the angle value for trig functions, or enter any two known values (sides or angle) for right triangle solving.
- Press the Calculate button to compute all trigonometric values or solve the complete right triangle.
- View all six trigonometric function values, inverse functions, or the complete triangle solution with all sides and angles.
Key Features
All Six Functions
Computes sin, cos, tan and their reciprocals csc, sec, cot for any angle value in one click.
Degrees and Radians
Switch between degree and radian input seamlessly. Results display in both units for convenience.
Right Triangle Solver
Enter any two known values and solve for all remaining sides and angles of a right triangle.
High Precision
Results accurate to 10 decimal places using IEEE 754 double-precision floating point math.
Instant Results
All calculations happen instantly in your browser with zero server requests or processing delays.
Works Everywhere
Fully responsive design works on smartphones, tablets and desktop computers across all browsers.
Trigonometric Formulas and How They Work
Trigonometry is built on the relationships between the sides and angles of triangles. In a right triangle with angle θ, the three primary trigonometric functions are defined as ratios of the triangle's sides.
sin(θ) = Opposite / Hypotenusecos(θ) = Adjacent / Hypotenusetan(θ) = Opposite / Adjacent = sin(θ) / cos(θ)The three reciprocal functions are derived directly from these primary ratios:
csc(θ) = 1 / sin(θ) = Hypotenuse / Oppositesec(θ) = 1 / cos(θ) = Hypotenuse / Adjacentcot(θ) = 1 / tan(θ) = Adjacent / Oppositeθ (theta): The angle being evaluated, measured in degrees or radians.
Opposite: The side directly across from angle θ.
Adjacent: The side next to angle θ (not the hypotenuse).
Hypotenuse: The longest side, opposite the 90° angle.
For the right triangle solver, the Pythagorean theorem connects all three sides:
a² + b² = c²where c = hypotenuse, a = opposite, b = adjacentDegree to radian conversion uses the formula: radians = degrees × (π / 180). Conversely, degrees = radians × (180 / π).
Practical Examples
🇮🇳 Arjun — Pune, India
Arjun is a Class 11 student preparing for JEE. He needs to find all trig values for 60°.
Input: Angle = 60°, Mode = Trig Functions
Result: sin(60°) = 0.8660254038, cos(60°) = 0.5, tan(60°) = 1.7320508076, csc(60°) = 1.1547005384, sec(60°) = 2, cot(60°) = 0.5773502692
Verified: sin(60°) = √3/2 ≈ 0.866 ✓
🇮🇳 Meera — Jaipur, India
Meera is an architecture student calculating the height of a ramp. She knows the ramp length (hypotenuse) is 5 metres and the angle of incline is 30°.
Input: Right Triangle mode, Side c = 5, Angle A = 30°
Result: Side a (height) = 2.5 m, Side b (base) = 4.3301 m, Angle B = 60°
Verified: sin(30°) × 5 = 0.5 × 5 = 2.5 ✓
🇺🇸 David — Chicago, USA
David is a physics student working with radians. He needs trig values for π/4 radians.
Input: Angle = 0.7853981634 rad (π/4), Mode = Radians
Result: sin(π/4) = 0.7071067812, cos(π/4) = 0.7071067812, tan(π/4) = 1.0
Verified: sin(π/4) = √2/2 ≈ 0.7071 ✓
🇮🇳 Kavitha — Chennai, India
Kavitha knows two sides of a right triangle: a = 3 and b = 4. She needs to find the hypotenuse and all angles.
Input: Right Triangle mode, Side a = 3, Side b = 4
Result: Side c = 5, Angle A = 36.8699°, Angle B = 53.1301°
Verified: 3² + 4² = 9 + 16 = 25 = 5² ✓
What Is a Trigonometry Calculator?
A trigonometry calculator is a mathematical tool that computes the values of trigonometric functions — sine, cosine, tangent, cosecant, secant, and cotangent — for any given angle. It also handles inverse trigonometric operations and can solve right triangles when provided with partial information.
Trigonometry is fundamental to fields ranging from engineering and physics to architecture and game development. Whether you're calculating the trajectory of a projectile, designing a roof angle, or solving homework problems, a trig calculator eliminates manual computation errors and saves significant time.
This calculator processes everything client-side in your browser. No data is sent to any server, which means it works offline after the page loads and your inputs remain completely private. It handles edge cases like tan(90°) where the function is mathematically undefined, displaying appropriate messages instead of incorrect values.
Want a deeper understanding of trigonometric functions and their applications?
Read Our Complete Guide to Trigonometry →Frequently Asked Questions
Is this tool free to use?
Yes, the Trigonometry Calculator is completely free with no limits on calculations. There are no signups or hidden charges.
What is the difference between degrees and radians?
Degrees divide a full circle into 360 parts, while radians use the ratio of arc length to radius. A full circle is 360 degrees or 2π radians. To convert degrees to radians, multiply by π/180.
How do I calculate sin, cos, and tan?
Enter any angle value, select degrees or radians, and click Calculate. The tool instantly computes sin, cos, tan, and their reciprocals (csc, sec, cot) for that angle.
What are inverse trigonometric functions?
Inverse trigonometric functions (arcsin, arccos, arctan) find the angle when you know the ratio. For example, arcsin(0.5) returns 30 degrees because sin(30°) = 0.5.
Can I solve a right triangle with this calculator?
Yes. Switch to Right Triangle mode, enter any two known values (two sides, or one side and one angle), and the calculator solves for all remaining sides and angles.
Why does tan(90°) show undefined?
Tangent equals sin divided by cos. At 90 degrees, cos(90°) equals zero, making the division undefined. The calculator correctly displays this as Undefined.
How accurate are the results?
Results are accurate to 10 decimal places using JavaScript's built-in Math functions, which follow the IEEE 754 double-precision standard.
What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
Can I use this calculator on my phone?
Yes, the calculator is fully responsive and works on all smartphones, tablets, and desktop browsers without any installation.
What is SOH CAH TOA?
SOH CAH TOA is a mnemonic for remembering trigonometric ratios. SOH: Sin = Opposite/Hypotenuse. CAH: Cos = Adjacent/Hypotenuse. TOA: Tan = Opposite/Adjacent.
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