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Stretching the Wave

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 17 of 51.

A b between 0 and 1 slows the angle down. In y = sin(x/2) the inside is only half of x, so it reaches 2π when x reaches 4π: one wave is twice as long as before.

$y = sin(x/2), one wave 4π long, over y = sin x$

The rule is the same: dividing by 2 is multiplying by b = 1/2, and 2pi/(1/2) = 4pi. The top comes a quarter of the way along, at π, instead of at π/2.

So for b positive, a b bigger than 1 squeezes the wave and a b between 0 and 1 stretches it. Either way the heights stay between −1 and 1.

Challenge

Draw the graph on the goal row. Press Check.

Try it yourself

y=sin(x/3)

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

1From Circle to Wave

Ride a Ferris Wheel Height on the Unit Circle Unrolling the Sine Graph The Sine Graph in Radians Circle to Wave Recap

4Period

Period: One Wave LongStretching the WavePeriod in Degrees b Is Not the Period Period Recap

7Reading a Graph

The Equation of a Wave Sine or Cosine?From Peaks to a Wave All Four at Once Reading Recap

10Final Challenges

A Wave From Its Facts A Hidden Shift A Flipped Tangent Read the Whole Wave Giant Wheel: the Model Giant Wheel: the Height

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 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