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The Midline

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 21 of 51.

Add a number outside the sine and every height goes up by it. y = sin(x) + 2 is the sine wave lifted 2: it now swings between 1 and 3, around the line y = 2.

$y = sin x + 2 swinging between 1 and 3 around the dashed line y = 2$

That line is the midline. For y = a×sin(x) + k with a positive, the midline is y = k, the top is k + a and the bottom is k − a. The wave crosses its midline where the plain sine crosses the x axis.

A negative k moves the wave down: y = sin(x) - 3 swings between −4 and −2.

Challenge

Draw the graph on the goal row. Press Check.

Try it yourself

y=2cos(x)-1

Draw the graph

Test yourself

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

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3Amplitude

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6Phase Shift

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9Modelling with Waves

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