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Chapter 6: Q. 29 (page 409)

In Problems 21鈥�30, match the given function to one of the graphs (A)鈥� (J).

y=3sin2x

Short Answer

Expert verified

The graph of the given function is graph (J)

Step by step solution

01

Step 1. Given information 

The trigonometric function is:y=3sin2x

02

Step 2. To determine the amplitude and period of the sinusoidal function.   

By comparing given function 3sin2xwith standard sine function: Asin蝇x

We get amplitude A=3

Time period is T=2蟺蝇T=2蟺2T=蟺

So the graph of the given function will have time period 蟺and amplitude 2

03

Step 3. To find passing points of the graph.

At y-axis

x=0

then y=3sin2.0y=3sin0y=3.0y=0

graph will pass through (0,2)

when x=蟺4

then

y=3sin2.蟺4y=3sin蟺2y=3.1y=3

graph will pass through蟺4,3

Now look at the given graphs from A-J in which

amplitude is 3, time period is蟺and passing point (0,2) and 蟺4,3

So the graph for given function is graph (J)

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