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All Common Core: High School - Functions Resources

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

What is the period of the following function?

$y=\sin(2x)$

$2\pi$

$\frac{\pi}{2}$

$\pi$

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

What is the period of the following function?

$y=\sin(2x)$

Your answer:

$2\pi$

Your answer:

$\frac{\pi}{2}$

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 period.

Given the function

$y=\sin(2x)$

identify the variables of the general form.

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

Step 3: Graph the trigonometric function to verify.

Screen shot 2016 01 19 at 6.51.48 am

The graph above verifies that the period of this function is $\pi$ because the flow of the graph only begins to repeat its cycle after $\pi$ units on the - axis.

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

What is the amplitude of the following function?

$y=2\sin(x)$

$\frac{\pi}{2}$

$2\pi$

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

What is the amplitude of the following function?

$y=2\sin(x)$

Your answer:

$\frac{\pi}{2}$

Your answer:

$2\pi$

Correct answer:

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 amplitude.

Given the function

$y=2\sin(x)$

identify the variables of the general form.

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

Step 3: Graph the trigonometric function to verify.

The graph above verifies that the amplitude of this function is two because the range of the function on the graph goes from negative two to positive two meaning the distance from zero at its highest peak or lowest valley is two.

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All Common Core: High School - Functions Resources

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

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

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

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

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