Trigonometry Calculator
Calculate sin, cos, tan, and all trig functions in degrees or radians
Trigonometry Calculator
Calculate sin, cos, tan and their inverses
Enter an angle in degrees to get all trig functions
sin(x), cos(x), tan(x) where x is in radiansWhat is a Trigonometry Calculator?
A Trigonometry Calculator is a math tool that helps you compute trigonometric values and solve trig-related problems involving angles and triangles. Trigonometry is the branch of mathematics that studies relationships between angles and side lengths of triangles, especially right triangles. The most common trigonometric functions are sine (sin), cosine (cos), and tangent (tan).
Trigonometry is used in many real-world fields, including physics, engineering, architecture, surveying, navigation, computer graphics, and signal processing. It helps calculate heights and distances, model waves, analyze motion, and solve geometry problems that involve angles.
Because trig calculations often involve decimals, special constants like π (pi), and different angle measurement systems (degrees and radians), a trigonometry calculator makes it easy to get accurate results quickly—without needing to memorize tables or do manual computations.
How to Use This Trigonometry Calculator
- Choose the trig function -- sin, cos, tan, and optionally inverse functions like sin⁻¹, cos⁻¹, tan⁻¹
- Enter the angle value -- for example: 30, 45, 60, or π/6 if your calculator supports π input
- Select the angle mode -- this calculator accepts input in Degrees (the value is automatically converted to radians internally)
- Click 'Calculate' -- to get the result
- Review the output -- and use it in your equation, triangle problem, or formula
Degrees vs Radians
This calculator accepts angles in degrees. Internally, the value is converted to radians using the formula: radians = degrees × (π / 180).
- Degrees are common in basic geometry and many real-life measurement problems
- Radians are standard in calculus, physics, and higher-level math
- If a result seems wrong, the most common cause is confusing degrees and radians
Tips:
- Enter angle values in degrees (e.g., 30, 45, 60, 90)
- tan(90°) is undefined because cos(90°) = 0 (division by zero)
- Use inverse trig functions when you know side ratios and need to find the angle
Trigonometry Formulas
Right Triangle Definitions (SOH-CAH-TOA)
In a right triangle relative to an angle θ:
- sin(θ) = opposite / hypotenuse (SOH)
- cos(θ) = adjacent / hypotenuse (CAH)
- tan(θ) = opposite / adjacent (TOA)
Inverse Trigonometric Functions
Inverse functions "undo" trig functions and return an angle:
- θ = sin⁻¹(opposite / hypotenuse)
- θ = cos⁻¹(adjacent / hypotenuse)
- θ = tan⁻¹(opposite / adjacent)
Pythagorean Identity
A fundamental trig identity:
sin²(θ) + cos²(θ) = 1
Holds true for every angle
Degrees and Radians Conversion
Degrees → Radians: Radians = Degrees × (π / 180)
Radians → Degrees: Degrees = Radians × (180 / π)
Common conversions:
Example Calculations
Example 1: Calculate sin(30°)
Input: Angle = 30°
sin(30°): 0.5
Result: 0.5
Example 2: Calculate cos(60°)
Input: Angle = 60°
cos(60°): 0.5
Result: 0.5
Example 3: Calculate tan(45°)
Input: Angle = 45°
tan(45°): 1
Result: 1
Example 4: Find an angle using inverse trig
Problem: A right triangle has opposite = 5 and adjacent = 5
Calculation: tan(θ) = opposite / adjacent = 5 / 5 = 1
Inverse: θ = tan⁻¹(1) = 45°
Result: θ = 45°
Frequently Asked Questions
What's the difference between degrees and radians?
Degrees divide a full circle into 360 parts, while radians measure angles based on the radius of a circle. A full circle is 360° or 2π radians. Radians are used more often in advanced math and physics.
Why does my trig answer look wrong?
The most common reason is the angle mode. For example, sin(30) in degrees is 0.5, but sin(30) in radians is about −0.988. Make sure the calculator is set to the correct mode—this calculator uses degrees by default.
What is SOH-CAH-TOA?
It's a memory aid for right triangle trigonometry:
- SOH: sin = opposite / hypotenuse
- CAH: cos = adjacent / hypotenuse
- TOA: tan = opposite / adjacent
When should I use inverse trig functions?
Use inverse trig when you know side ratios (or side lengths) and need to find the angle. For example, if you know opposite and adjacent sides, use tan⁻¹.
Can trigonometry be used for non-right triangles?
Yes. For non-right triangles, trig uses the Law of Sines and Law of Cosines. Some trig calculators include these features; if yours does, you can solve for missing sides or angles in any triangle.
Want to add this trigonometry calculator to your website? Get a custom embed code that matches your site's design and keeps visitors engaged.
What Is Trigonometry?
Trigonometry is the branch of mathematics that studies the relationships between the angles and sides of triangles. It forms the backbone of countless fields: navigation uses it to plot courses, physics uses it to resolve forces, engineers rely on it to design structures, architects use it for roof pitches and arches, and computer graphics use it to rotate and project 3D objects onto 2D screens. Mastering trig means mastering the geometry of the world around you.
The six fundamental trigonometric functions — sine, cosine, tangent, cosecant, secant, and cotangent — describe ratios between pairs of sides in a right triangle relative to a given angle. This calculator lets you compute any of those six functions instantly for any angle in degrees or radians. It also handles the inverse functions (arcsin, arccos, arctan), which work backwards: give them a ratio and they return the angle that produces it.
How to Use the Trigonometry Calculator
- Choose your angle unit — degrees for everyday geometry, radians for calculus and physics.
- Select the function you need: sin, cos, tan, csc, sec, cot, or an inverse (arcsin, arccos, arctan).
- Enter the angle value (for direct functions) or the ratio value (for inverse functions).
- Read your result instantly — no rounding, full decimal precision shown.
Trigonometry Formulas
sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent = sin(θ)/cos(θ)
csc(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), cot(θ) = 1/tan(θ)
Inverse: arcsin(x), arccos(x), arctan(x)
Pythagorean identity: sin²(θ) + cos²(θ) = 11 radian = 180°/π ≈ 57.296°. Most scientific and engineering contexts express angles in radians because it simplifies calculus and wave equations. Everyday geometry — construction, surveying, navigation — typically sticks to degrees. Knowing how to convert between the two is an essential skill.
Worked Examples
Example 1: sin(45°)
sin(45°) = √2 / 2 ≈ 0.7071. A 45° angle sits exactly halfway up the first quadrant, and its sine and cosine are equal — both equal to the square root of 2 divided by 2. This value appears constantly in geometry, physics, and signal processing.
Example 2: cos(60°)
cos(60°) = 0.5. At 60°, the adjacent side is exactly half the hypotenuse. This clean ratio makes 30-60-90 triangles one of the most useful shapes in engineering and architecture — the half-cosine relationship is why 60° corners are so common in structural design.
Example 3: arctan(1) = 45°
arctan(1) = 45°. When the tangent ratio equals 1, the opposite and adjacent sides are equal, meaning the angle is precisely 45°. Inverse trig functions like arctan are used whenever you know a ratio and need to recover the angle — for example, finding the slope angle of a ramp or the bearing of a ship.