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Amplitude of a Cosine

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 10 of 49.

The same holds for the cosine. $y = 2\cos\left(x\right)$ 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. $y = 0.8\cos\left(x\right)$ 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 = \frac{3}{2}\cos x

Draw the wave

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

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5Midline

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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