Trigonometry Calculator

Simplify trigonometric expressions, solve equations, and evaluate functions.

Our Trigonometry Calculator is your swiss-army knife for trig problems. Simplify complex identities, find solutions to trigonometric equations, and evaluate functions effortlessly.

✓ Simplify Identities✓ Solve Equations✓ Interactive Graphs

Enter Expression or Equation

Trig Expression

Examples:

Graph Visualization

Result

\sin(x)^2 + \cos(x)^2 = 1

What is Trigonometry Calculator?

Trigonometry examines the relationship between the angles and sides of triangles. It's built on points on a circle (Sine and Cosine).

Key functions include:

Sine ($\sin$): Opposite / Hypotenuse
Cosine ($\cos$): Adjacent / Hypotenuse
Tangent ($\tan$): Opposite / Adjacent ($\sin/\cos$)

Formula & Calculation

Fundamental Identities

Pythagorean

\sin^2 \theta + \cos^2 \theta = 1

Quotient

\tan \theta = \frac{\sin \theta}{\cos \theta}

Reciprocal

\sec \theta = \frac{1}{\cos \theta}, \csc \theta = \frac{1}{\sin \theta}

Double Angle

\sin(2\theta) = 2\sin\theta\cos\theta

Example Calculation

Simplification Example

Simplify $(\sin x + \cos x)^2 + (\sin x - \cos x)^2$

Expand both terms:

(\sin^2 + 2\sin\cos + \cos^2) + (\sin^2 - 2\sin\cos + \cos^2)

Combine like terms ($2\sin\cos$ cancels out):

2\sin^2 x + 2\cos^2 x = 2(\sin^2 x + \cos^2 x) = 2(1) = 2

Related Tools

Frequently Asked Questions

Why are there multiple solutions for sin(x) = 0.5?

Trigonometric functions are periodic (they repeat). $\sin(30^\circ) = 0.5$, but so is $\sin(150^\circ)$, $\sin(390^\circ)$, etc. The solutions are infinite unless a range is specified.

What is the difference between specific and general solutions?

A specific solution might be $x = 30^\circ$. A general solution accounts for all repetitions, like $x = 30^\circ + 360^\circ n$ where $n$ is an integer.