Trig Calculator

Introduction

This trig calculator helps you quickly solve trigonometric functions like sine, cosine, and tangent. Trigonometry is a branch of math that deals with the relationships between the sides and angles of triangles. Whether you are working on homework, studying for a test, or solving real-world problems, this tool gives you fast and accurate answers. Just enter your values, and the calculator does the rest. It works with all six trig functions: sine, cosine, tangent, cosecant, secant, and cotangent. You can use degrees or radians depending on what you need.

How to use our Trig Calculator

This calculator lets you enter a trigonometric function and an angle to quickly find the result. Just pick your function, type in your angle, and choose your angle unit to get an instant answer.

Function: Select the trig function you want to solve. You can choose from sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), or cotangent (cot). Inverse functions like arcsin, arccos, and arctan are also available.

Angle Value: Enter the number for your angle. This can be any positive or negative number, including decimals.

Angle Unit: Choose whether your angle is in degrees or radians. Most school problems use degrees, but radians are common in advanced math and science.

What Is Trigonometry?

Trigonometry is a branch of math that studies the relationships between the angles and sides of triangles. The word comes from Greek and means "triangle measurement." At its core, trigonometry uses six main functions — sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot) — to connect an angle to a ratio of two sides in a right triangle.

The Six Trig Functions

In a right triangle, one angle is always 90 degrees. The other two angles are acute, meaning they are less than 90 degrees. Every trig function takes one of those acute angles and gives you a ratio:

• sin(θ) = opposite side ÷ hypotenuse
• cos(θ) = adjacent side ÷ hypotenuse
• tan(θ) = opposite side ÷ adjacent side
• csc(θ) = hypotenuse ÷ opposite side (the flip of sin)
• sec(θ) = hypotenuse ÷ adjacent side (the flip of cos)
• cot(θ) = adjacent side ÷ opposite side (the flip of tan)

The hypotenuse is the longest side of a right triangle, sitting across from the right angle. The opposite side is across from the angle you are looking at, and the adjacent side is next to it.

Degrees, Radians, and Gradians

Angles can be measured in different units. Degrees split a full circle into 360 parts. Radians use the radius of a circle as a measuring stick — a full circle equals 2π radians (about 6.2832). Gradians split a full circle into 400 parts. Most school problems use degrees, while higher math and science tend to use radians.

Common Angle Values

Certain angles show up again and again in math: 0°, 30°, 45°, 60°, and 90°. These angles have exact trig values that are worth memorizing. For example, sin(30°) = 1/2, cos(45°) = √2/2, and tan(60°) = √3. Knowing these by heart saves time and helps you check your work. You can verify these values using a square root calculator for expressions like √2/2 and √3/2.

Right Triangle Solving

If you know any two measurements of a right triangle — two sides, or one side and one acute angle — you can find everything else. This is called solving the triangle. The Pythagorean theorem (a² + b² = c²) connects the three sides, while trig functions connect sides to angles. From a solved triangle, you can also find its area (½ × base × height) using a triangle area calculator, perimeter (sum of all sides), and the altitude drawn to the hypotenuse. For non-right triangles, you can use the Law of Sines calculator or the Law of Cosines calculator to solve for unknown sides and angles.

Inverse Trig Functions

Sometimes you know the ratio but need the angle. That is where inverse trig functions come in. Written as asin, acos, and atan (also called arcsin, arccos, and arctan), these take a number and return an angle. For example, asin(0.5) = 30° because sin(30°) = 0.5. Inverse functions have domain limits — asin and acos only accept inputs between −1 and 1. Understanding fractions and decimal-to-fraction conversions can help when working with these ratios.

Trig Identities

Trig identities are equations that are true for every angle. The most important one is the Pythagorean identity: sin²(θ) + cos²(θ) = 1. This means no matter what angle you pick, if you square its sine and cosine and add them together, you always get 1. Other useful identities include sec²(θ) − tan²(θ) = 1 and csc²(θ) − cot²(θ) = 1. These identities help simplify complex expressions and verify calculations. Working with powers in these identities is easier with an exponent calculator, and if you need to find the slope of a line using tangent, trig plays a key role there too. Trigonometric functions also appear frequently in derivatives and integrals in calculus.

Frequently Asked Questions

What is a trig calculator?

A trig calculator is a tool that finds the values of trigonometric functions like sine, cosine, and tangent for any angle you enter. It can also solve right triangles and evaluate trig expressions. You type in an angle or a value, and the calculator gives you the answer right away.

Can I enter a negative angle?

Yes. You can type any positive or negative angle into the calculator. Negative angles measure rotation in the clockwise direction. The calculator will still give you correct values for all six trig functions.

What is the difference between degrees and radians?

Degrees split a full circle into 360 equal parts. Radians use the radius of a circle as the unit, so a full circle equals about 6.2832 radians (2π). To switch between them, multiply degrees by π/180 to get radians, or multiply radians by 180/π to get degrees.

What are gradians?

Gradians split a full circle into 400 equal parts. A right angle is 100 gradians instead of 90 degrees. Gradians are mostly used in surveying and some engineering fields. This calculator supports gradians as an angle unit option.

Why does the calculator say undefined for some values?

Some trig functions are undefined at certain angles. For example, tan(90°) is undefined because you would be dividing by zero. The same happens with csc(0°), sec(90°), and cot(0°). When this occurs, the calculator shows "undefined" instead of a number.

How do I use the reverse-solve feature in the Trig Function Evaluator?

Instead of entering an angle, you can type a value into any trig function field. For example, type 0.5 into the sin(θ) field, and the calculator will find the angle whose sine is 0.5 (which is 30°). It then fills in all the other function values for that angle.

How many values do I need to solve a right triangle?

You need at least two known values to solve a right triangle. This can be two sides, or one side and one acute angle. The calculator uses the Pythagorean theorem and trig functions to find all the missing sides, angles, area, perimeter, and altitude.

Why can't I solve a right triangle with just two angles?

Two angles alone tell you the shape of the triangle but not its size. Since one angle is always 90°, knowing one acute angle automatically gives you the other. Without at least one side length, there are infinitely many triangles that could match. You must provide at least one side.

What does the Expression Solver do?

The Expression Solver lets you type in a full trig expression like sin(30)^2 + cos(30)^2 and get the answer. It breaks the problem into steps so you can see how each part is calculated. You can use sin, cos, tan, cot, sec, csc, and their inverse functions, plus sqrt, pi, and powers.

How do I type powers and square roots in the Expression Solver?

Use the ^ symbol for powers. For example, type sin(45)^2 to square the sine of 45. For square roots, type sqrt() with the number inside the parentheses, like sqrt(3) for √3.

What does the Exact value mean?

An exact value shows the answer as a simple fraction or root instead of a long decimal. For example, sin(30°) has an exact value of 1/2, which is more precise than 0.5000. Exact values are available for common angles like 0°, 30°, 45°, 60°, 90°, and their multiples.

What is the altitude to the hypotenuse?

The altitude to the hypotenuse is a line drawn from the right angle straight down to the hypotenuse. It splits the triangle into two smaller right triangles. The calculator finds this value using the formula: altitude = (side a × side b) ÷ hypotenuse.

Can I use pi in the Expression Solver?

Yes. Type pi or the π symbol to use the value of pi (approximately 3.14159). For example, you can type sin(pi/6) when working in radians to get the sine of 30°.

How accurate are the results?

The calculator shows results up to 10 decimal places. This level of precision is more than enough for homework, tests, and most real-world applications. For common angles, the calculator also displays exact values with no rounding at all.

What is the Common Angles Reference Table?

The reference table lists all six trig function values for angles that appear most often in math: 0°, 30°, 45°, 60°, 90°, and so on up to 360°. It shows both exact values and their radian equivalents. Click the section header to expand and view the full table.