Menu

English

Amplitude: How Tall

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 11 of 51.

Multiply the sine by a number and every height is multiplied with it. In y = 3sin(x) the top is 3 instead of 1 and the bottom is −3. The zeros stay where they were, because 3 × 0 is still 0.

$y = 3 sin x over y = sin x: the same zeros, three times as tall$

The distance from the middle of a wave to its top is its amplitude. For y = a×sin(x) or y = a×cos(x) the amplitude is the size of a: 3 here. That is half the full height of the wave, which runs 6 from bottom to top.

A number between 0 and 1 squashes the wave instead: y = 1/2×sin(x) only reaches 1/2.

Challenge

Draw the graph on the goal row. Press Check.

Try it yourself

y=4sin(x)

Draw the graph

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 TallAmplitude of a Cosine A Negative a Flips It Amplitude From a Graph Amplitude 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