Trigonometry Calculator
Free Trigonometry Calculator for math. Enter values to solve step-by-step with verified formulas, worked examples, and detailed explanations.
Formula
sin(θ) = Opp/Hyp
Trigonometric functions relate angles to side ratios in right triangles.
Worked Examples
Example 1: Sin(30°)
Problem:Angle 30 degrees
Solution:Opposite side is half the hypotenuse.
Result:0.5
Example 2: Tan(45°)
Problem:Angle 45 degrees
Solution:Opposite equals Adjacent.
Result:1
Frequently Asked Questions
What is Trigonometry?
It is the branch of mathematics dealing with the relationships between the sides and angles of triangles.
What is SOH CAH TOA?
It is a memory aid for right triangle ratios: Sin = Opp/Hyp, Cos = Adj/Hyp, Tan = Opp/Adj.
What is a Radian?
A radian is the standard unit of angular measure, used in many areas of mathematics. 1 radian is the angle where the arc length equals the radius.
What is the Unit Circle?
A circle with a radius of 1 centered at (0,0). It allows trigonometric functions to be defined for all real numbers, not just acute angles.
Why is Tan(90°) undefined?
Tan(θ) = y/x. At 90°, the coordinate on the unit circle is (0,1). Division by zero (1/0) is undefined.
What are Inverse Trig Functions?
Functions like arcsin, arccos, and arctan work backwards: you give them a ratio (side length), and they give you the angle.
What is the Pythagorean Identity?
sin²(θ) + cos²(θ) = 1. This is true for any angle θ and is derived from the Pythagorean theorem on the unit circle.
What are the Reciprocal Functions?
Cosecant (csc = 1/sin), Secant (sec = 1/cos), and Cotangent (cot = 1/tan).
How is trigonometry used in real life?
It is used in architecture, engineering, astronomy, music production (sound waves), game development (graphics), and navigation.
Background & Theory
Trigonometric Functions:
Relate the angles of a right triangle to the ratios of its side lengths.
Primary Ratios (SOH CAH TOA):
- Sine (sin θ): Opposite / Hypotenuse
- Cosine (cos θ): Adjacent / Hypotenuse
- Tangent (tan θ): Opposite / Adjacent
Unit Circle:
A circle with radius 1 centered at the origin.
- x-coordinate = cos(θ)
- y-coordinate = sin(θ)
Modes:
- Degrees: Circle = 360°
- Radians: Circle = 2π radians (approx 6.28)