Amplitude of a Cosine

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 12 of 51.

The same holds for the cosine. y = 2cos(x) starts at its top, 2 at 0°, falls to −2 at 180° and is back at 2 at 360°. Its amplitude is 2.

$y = 2 cos x over y = cos x on a degree axis$

A common slip is to read the amplitude as the full height of the wave, 4 here, from −2 up to 2. The amplitude is measured from the middle line to the top, so it is half of that.

Any size works. y = 0.8cos(x) has its top at 0.8 and its bottom at −0.8.

Challenge

Draw the graph on the goal row. Heights snap to halves. Press Check.

Try it yourself

y=3/2cos(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 CosineA 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