Explore Trigonometric Graphs

Visualize the behavior of sine, cosine and tangent functions. Understand amplitude, period, domain and range through interactive graphs.

Sine Wave Preview

Function Graphs

π

Sine Graph

y = sin(x)

The sine graph produces a smooth repeating wave. Its values range from -1 to 1.

θ

Cosine Graph

y = cos(x)

The cosine graph is similar to sine but begins at its maximum value.

tan

Tangent Graph

y = tan(x)

The tangent graph contains repeating vertical asymptotes.

Triangles and Formulas

01

SOH CAH TOA

A handy memory aid to remember ratios: Sine is Opposite/Hypotenuse, Cosine is Adjacent/Hypotenuse, and Tangent is Opposite/Adjacent.

02

The Hypotenuse

The longest side of a right-angled triangle. It is always located directly opposite the 90-degree right angle.

03

Degrees vs Radians

Angles can be measured in degrees (0 to 360) or radians (0 to 2π). A complete circle is exactly 360° or 2π radians.

04

Pythagorean Connection

Right triangles follow the formula a² + b² = c². Therefore, sin²(θ) + cos²(θ) = 1.

05

Periodic Behavior

Sine and Cosine are repeating wave cycles. Their values repeat continuously between -1 and 1.

06

Tangent Limits

Because tangent equals Opposite ÷ Adjacent, when the adjacent side becomes zero, tangent approaches infinity and becomes undefined.

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Learn Trigonometry by Watching

Watch these carefully selected lessons to understand trigonometric functions, graphs, identities and the unit circle.

r = 1 The Unit Circle
Standard Radius
90° Right Angle (π/2 Radians)
180° Straight Line (π Radians)
360° Full Rotation (2π Radians)