How to find the midline of a trig function?
Understand the Problem
The question is asking for the method to determine the midline of a trigonometric function, which involves identifying the vertical shift of the function from its center position.
Answer
The midline of a trigonometric function is given by $y = D$, where $D$ is the vertical shift.
Answer for screen readers
The midline of the function is given by the equation $y = D$, where $D$ is the vertical shift of the function.
Steps to Solve
- Identify the function Check the trigonometric function you are given. It usually takes the form of $y = A \cdot \sin(B(x - C)) + D$ or $y = A \cdot \cos(B(x - C)) + D$, where:
- $A$ is the amplitude,
- $B$ affects the period,
- $C$ is the phase shift,
- $D$ is the vertical shift.
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Locate the vertical shift The midline of the trigonometric function is determined by the vertical shift, which is represented by the value $D$ in the equation. This value indicates how much the graph shifts up or down from the x-axis.
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State the midline equation The midline of the trigonometric function can be expressed as the equation $y = D$. Thus, once you identify $D$, you can write the midline equation.
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Example For the function $y = 2 \cdot \sin(x) + 3$, the vertical shift is $D = 3$. Hence, the midline equation is $y = 3$.
The midline of the function is given by the equation $y = D$, where $D$ is the vertical shift of the function.
More Information
The midline is important because it represents the average position of the function, dividing the oscillations evenly. It helps in analyzing the behavior and amplitude of the trigonometric function.
Tips
- Forgetting to identify the correct form of the function can lead to incorrect identification of the vertical shift.
- Mistakenly interpreting the amplitude $A$ as the midline instead of the vertical shift $D$.
