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Q27.

Expert-verified

Algebra 2

Found in: Page 767

Book edition Middle English Edition

Author(s) Carter

Pages 804 pages

ISBN 9780079039903

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Short Answer

Find the amplitude if it exists and period of the function $y = 6 \sin (\frac{2 θ}{3})$ and then graph the function.

The amplitude of $y = 6 \sin (\frac{2 θ}{3})$ is 6.

The period of $y = 6 \sin (\frac{2 θ}{3})$ is $3 π$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Write down the given information.

The given function is $y = 6 \sin (\frac{2 θ}{3})$ .

Step 2. Concept used.

A function of the form $y = a \sin (b x) and y = a \cos (b x)$ has amplitude of $|a|$ and period $\frac{360 °}{|b|} or \frac{2 π}{|b|}$ .

Step 3. Evaluating amplitude and period of the given function.

With the help of concept stated above, the amplitude and period of the function is evaluated as:

The amplitude of $y = 6 \sin (\frac{2 θ}{3})$ is $|6| = 6$ .

The period of $y = 6 \sin (\frac{2 θ}{3})$ is $\frac{2 π}{|\frac{2}{3}|} = 3 π$ .

Step 4. Sketch the graph for the function.

The graph for the function $y = 6 \sin (\frac{2 θ}{3})$ is shown below.

Step 5. Conclusion.

The amplitude of $y = 6 \sin (\frac{2 θ}{3})$ is 6.

The period of $y = 6 \sin (\frac{2 θ}{3})$ is $3 π$ .

Most popular questions for Math Textbooks

Find the amplitude if it exists and period of the function $y = \frac{1}{2} \sin (θ)$ and then graph the function.

How do the periods of the tuning forks compare?

Solve the equation $A r c c o s (\frac{\sqrt{2}}{2}) = x$ .

When represented on an oscilloscope, the note A above middle C has

period of $\frac{1}{440}$ . Which of the following can be an equation for an oscilloscope graph of this note? The amplitude of the graph is $K$ .

a. $y = K \sin 220 π t$

b. $y = K \sin 440 π t$

c. $y = K \sin 880 π t$

Write the equation of a trigonometric function with a phase shift of $- 45 °$ .

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