Trigonometry Calculator
Calculate sine, cosine, tangent, and their inverses. Solve right triangles and unit circle values.
About Trigonometry Calculator
A trigonometry calculator computes sine, cosine, tangent, and their inverse functions (arcsin, arccos, arctan), as well as solving right triangles and unit circle values. Trigonometry is essential in geometry, physics, engineering, navigation, architecture, and computer graphics. It relates the angles of a triangle to the lengths of its sides and extends to describe periodic phenomena like sound waves and light.
How to Use
Select the calculation mode: compute a specific trig function value, solve a right triangle (enter any two values to find the rest), or convert between degrees and radians. For function computation, enter the angle value and select the function. For triangle solving, enter two known values (sides and/or angles) and the calculator finds all remaining sides and angles.
Formula / Key Equations
SOH-CAH-TOA: sin(angle) = Opposite / Hypotenuse. cos(angle) = Adjacent / Hypotenuse. tan(angle) = Opposite / Adjacent. Pythagorean theorem: a squared + b squared = c squared. Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). Law of Cosines: c squared = a squared + b squared - 2ab×cos(C).
Common Use Cases
Solving right triangle problems in geometry and physics. Computing angles and distances in surveying and navigation. Analyzing wave patterns in sound and light. Designing structures and calculating roof pitches in architecture. Game development and computer graphics (rotation, projection). Electrical engineering (AC circuit analysis with phase angles).
Limitations
The primary trig functions are defined for angles from -360 to 360 degrees (or -2pi to 2pi radians). tan(x) is undefined at 90 degrees and 270 degrees (where cos(x) = 0). arcsin and arccos only accept values between -1 and 1. The right triangle solver assumes standard triangle geometry — degenerate triangles (where one side equals the sum of the other two) are not handled.
Frequently Asked Questions
What is SOH-CAH-TOA?
SOH-CAH-TOA is a mnemonic for remembering the three basic trigonometric ratios in a right triangle: Sine = Opposite/Hypotenuse (SOH), Cosine = Adjacent/Hypotenuse (CAH), Tangent = Opposite/Adjacent (TOA). These relate the angles to the side lengths of a right triangle.
When should I use degrees vs radians?
Degrees are used for everyday angle measurements (0-360) and are more intuitive for most people. Radians are the standard in higher mathematics, physics, and engineering because they simplify many formulas. One full circle = 360 degrees = 2pi radians.
How do I solve a triangle with only one known value?
A unique triangle requires at least 3 known values, including at least one side. With fewer values, multiple triangles are possible. For a right triangle, you need at least two values (sides and/or angles) to solve for all remaining unknowns.
What are the inverse trig functions?
Inverse trig functions (arcsin, arccos, arctan) do the opposite of regular trig functions — they find the angle when you know the ratio. For example, if sin(angle) = 0.5, then arcsin(0.5) = 30 degrees. They are also written as sin^(-1), cos^(-1), tan^(-1).
What is the unit circle?
The unit circle is a circle with radius 1 centered at the origin. For any angle, the point where the terminal side intersects the circle has coordinates (cos(angle), sin(angle)). The unit circle provides the values of trig functions for commonly used angles like 0, 30, 45, 60, and 90 degrees.
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