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Chapter 14: Q12. (page 767)

Find the amplitude if it exists and period of the function y=34cos胃2 and then graph the function.

Short Answer

Expert verified

The amplitude of y=34cos胃2is 34.

The period of y=34cos胃2 is 4蟺.

Step by step solution

01

Step 1. Write down the given information.

The given function is y=34cos胃2.

02

Step 2. Concept used.

A function of the form y=asinbxandy=acosbx has amplitude of a and period 360掳bor2蟺b.

03

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=34cos胃2is 34=34.

The period of y=34cos胃2 is 2蟺12=4蟺.

04

Step 4. Sketch the graph for the function.

The graph for the function y=34cos胃2 is shown below.

05

Step 5. Conclusion.

The amplitude of y=4cos3胃4is 34.

The period of y=34cos胃2 is 4蟺.

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