Trigonometry Calculator
Your all-in-one tool for triangles, circles, and trigonometric functions.
Right Triangle Solver
Enter any two values to solve for the rest.
Law of Sines & Cosines Solver
Enter any 3 values (e.g., SSS, SAS, ASA) to solve.
Trigonometric Functions
Interactive Unit Circle
Enter an angle or drag the point on the circle.
Coordinates & Values
Angle: 45° | π/4
(x, y): (0.707, 0.707)
sin(θ): 0.707
cos(θ): 0.707
tan(θ): 1.000
Angle Unit Converter
How to Solve Any Triangle Problem
Our calculator is designed to be your all-in-one trigonometry resource. Here's how to use each feature to solve your specific problem.
Right Triangle Solver
This is your go-to for any right-angled triangle. Simply enter any two known values (e.g., two sides, or one side and one angle) and the calculator will instantly find all missing sides, angles, area, and perimeter using SOH CAH TOA and the Pythagorean theorem.
Law of Sines & Cosines
For triangles that are not right-angled (oblique triangles), use this solver. It's perfect for solving cases like Side-Angle-Side (SAS), Side-Side-Side (SSS), or Angle-Side-Angle (ASA) by applying the appropriate laws.
Functions Calculator
A quick and powerful calculator for the six trigonometric functions (sin, cos, tan, etc.) and their inverses. Use the toggle to switch between Degrees (DEG) and Radians (RAD) for your calculations.
Interactive Unit Circle
Visualize how angles relate to (x, y) coordinates and trig functions. Drag the point on the circle or use the slider to change the angle and see the values for sine, cosine, and tangent update in real-time.
Angle Converter
Effortlessly convert between the three main units for measuring angles: Degrees, Radians, and Gradians. Enter a value in any field, and the other two will be calculated instantly.
Step-by-Step Solutions
For every triangle calculation, a solution card appears showing the exact formulas used (like a = sqrt(c² - b²)). This helps you learn the process, not just get the answer.
Trigonometry Questions Answered (FAQ)
How do you use SOH CAH TOA?
SOH CAH TOA is a mnemonic for the basic trigonometric ratios in a right triangle:
- SOH: Sin(θ) = Opposite / Hypotenuse
- CAH: Cos(θ) = Adjacent / Hypotenuse
- TOA: Tan(θ) = Opposite / Adjacent
Use it when you know two sides and want to find an angle, or when you know one side and one angle and want to find another side.
When do you use the Pythagorean Theorem?
Use the Pythagorean Theorem (a² + b² = c²) in a right triangle when you know the lengths of two sides and need to find the third. It only works for right triangles.
What is the difference between Law of Sines and Law of Cosines?
Use the Law of Sines when you know a side and its opposite angle (a pair), plus one other piece of information (ASA, AAS, SSA cases). Use the Law of Cosines when you know two sides and the angle between them (SAS) or all three sides (SSS).
How do you find a missing side of a triangle?
For a right triangle, use SOH CAH TOA if you have an angle and a side, or the Pythagorean Theorem if you have two sides. For any other triangle (oblique), use the Law of Sines or Law of Cosines based on what information you have.
How do inverse trig functions work?
While a function like sin(30°) gives you a ratio (0.5), an inverse function (like sin⁻¹ or arcsin) does the opposite. It takes a ratio and gives you the angle. For example, sin⁻¹(0.5) gives you 30°. They are essential for finding unknown angles in a triangle.
What is the unit circle used for?
The Unit Circle is a circle with a radius of 1. It's a powerful tool for visualizing how trigonometric functions relate to angles and (x,y) coordinates. For any angle θ, the coordinate on the circle is (cos(θ), sin(θ)), which helps in understanding the sign and value of trig functions in different quadrants.