Trigonometry

Study of triangles and trigonometric functions including sine, cosine, and tangent.

Understanding Angles and TrianglesSine, Cosine, and Tangent FunctionsThe Unit Circle and Radian Measure
Trigonometric Identities and FormulasSolving TrianglesGraphs of Trigonometric Functions
Measuring Heights and DistancesTrigonometry in Engineering and DesignNavigation and GPS
Memorizing Trigonometric ValuesSolving Word Problems with DiagramsChecking Your Work with Inverse Functions
Understanding Angles...Sine, Cosine, and Ta...The Unit Circle and ...Trigonometric Identi...Solving TrianglesGraphs of Trigonomet...Measuring Heights an...Trigonometry in Engi...Navigation and GPSMemorizing Trigonome...Solving Word Problem...Checking Your Work w...
Advanced Topics

Graphs of Trigonometric Functions

Picture This: Sine, Cosine, and Tangent Graphs

Trigonometric functions aren't just numbers—they create beautiful, wavy graphs! The sine and cosine graphs are smooth curves that repeat every \(2\pi\) radians.

  • Sine graph starts at zero, goes up to 1, down to -1, and repeats.
  • Cosine graph starts at 1, goes down to -1, and repeats.
  • Tangent graph has a different shape, with repeating curves and vertical asymptotes.

These patterns help explain everything from sound waves to tides!

Examples

  • The height of a swinging pendulum can be modeled by a cosine graph.

  • The brightness of daylight through a year follows a sine wave pattern.

In a Nutshell

Graphs show how trig functions repeat in cycles and help model real-world phenomena.

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Measuring Heights and Distances