How to Find the Midline of a Sine Wave

Step-by-step solution

1. Find the number added outside the sine.

   $$+3$$

   Why: The term outside the function moves the whole graph up or down.

2. Name the vertical shift.

   $$D = 3$$

   Why: The graph of sin x sits between -1 and 1; adding 3 moves it to between 2 and 4.

3. Write the midline.

   $$y = 3$$

   Why: The midline is the horizontal line halfway between the highest and lowest points.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $y = \sin(x) + 2$

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   $y = 2$

2. 2

   $y = \cos(x) - 4$

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   $y = -4$

3. 3

   $y = 2\sin(x) + 1$

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   $y = 1$

4. 4

   $y = \cos(x) + 5$

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   $y = 5$

5. 5

   $y = \sin(x) - 1$

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   $y = -1$