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Amplitude From a Graph

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 14 of 51.

To read a from a wave of the form a sin x or a cos x, take its highest and lowest values: halfway between them is the middle line, 0, and the distance from there to the top is the amplitude. A wave from −3 to 3 has amplitude 3.

Then look at x = 0 to choose the function and the sign of a. At its top, it is a cosine with positive a; at its bottom, a cosine with negative a. On the axis going up, it is a sine with positive a; on the axis going down, a sine with negative a.

$A wave from -3 to 3 that crosses the axis going down at 0$

This wave runs from −3 to 3 and crosses 0 going down at x = 0, so it is y = -3sin(x).

Challenge

Write the equation of the wave in the graph tile in the form y = a×cos(x). Press Check.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Graphs of Trig Functions

2The Cosine Graph

Cosine: the Point's x The Cosine Graph Cosine Is a Shifted Sine Where Sine Meets Cosine Cosine Graph Recap

5Midline

The Midline From Highest and Lowest Reading the Midline Midline Recap

8The Tangent Graph

The Tangent Graph Asymptotes Stretching the Tangent Graphs of sec, csc and cot Tangent Recap

3Amplitude

Amplitude: How Tall Amplitude of a Cosine A Negative a Flips ItAmplitude From a GraphAmplitude Recap

6Phase Shift

Phase Shift: Sliding Phase Shift in Degrees Factor Out b First Reading a Phase Shift Phase Shift Recap

9Modelling with Waves

A Ferris Wheel Model Daylight Over a Year Tides Using a Model A Spring's Bounce Modelling Recap