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Common Core: High School - Functions : Model Periodicity, Amplitude, Frequency, and Midline of Trigonometric Functions: CCSS.Math.Content.HSF-TF.B.5

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Example Question #11 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

What is the vertical shift of the function?

$f(x)=\cos(x)+\pi$

Possible Answers:

$\pi$

$\frac{\pi}{2}$

$-\pi$

Correct answer:

$\pi$

Explanation:

This question is testing one's ability to identify the periodicity of a trigonometric function. This requires the understanding of trigonometric functions and their graphical and algebraic characteristics.

For the purpose of Common Core Standards, "Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline" falls within the Cluster B of "Model Periodic Phenomena with Trigonometric Functions" concept (CCSS.MATH.CONTENT.HSF-TF.B.5).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

$\\F(x)=\textup{New function after shift} \\a=\textup{Amplitude} \\b=\textup{period}\rightarrow \frac{2\pi}{|B|} \\ \\c=\textup{Horizontal shift} \\ d=\textup{Vertical shift} \\f(x)=\textup{Trigonometric function}$

Step 2: Algebraically identify the vertical shift.

Given the function

$y=\cos(x)+\pi$

identify the variables of the general form.

$\\f(x)=\cos \\a=1 \\b=1\rightarrow \frac{2\pi}{|1|}=2\pi \\c=0 \\d=\pi$

Step 3: Graph the trigonometric function to verify.

Q11

The graph above verifies that the vertical shift of the function is $\pi$ .

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Example Question #52 : Trigonometric Functions

What is the vertical shift of the function?

$f(x)=\cos(x)-\pi$

Possible Answers:

$\pi$

$-\pi$

$\frac{\pi}{2}$

Correct answer:

$-\pi$

Explanation:

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Write the general form of trigonometric shifts.

F(x)=af(bx-c)+d

where

Step 2: Algebraically identify the vertical shift.

Given the function

$y=\cos(x)-\pi$

identify the variables of the general form.

$\\f(x)=\cos \\a=1 \\b=1\rightarrow \frac{2\pi}{|1|}=2\pi \\c=0 \\d=-\pi$

Step 3: Graph the trigonometric function to verify.

Q12

The graph above verifies that the vertical shift of the function is $-\pi$ .

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Common Core: High School - Functions : Model Periodicity, Amplitude, Frequency, and Midline of Trigonometric Functions: CCSS.Math.Content.HSF-TF.B.5

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

Example Questions

Example Question #11 : Model Periodicity, Amplitude, Frequency, And Midline Of Trigonometric Functions: Ccss.Math.Content.Hsf Tf.B.5

Example Question #52 : Trigonometric Functions

All Common Core: High School - Functions Resources

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