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Chapter 6: Q. 34 (page 410)

In Problems 31鈥�34, match the given function to one of the graphs (A)鈥� (D).

y=-3sin12x

Short Answer

Expert verified

The graph of the given function is graph (D)

Step by step solution

01

Step 1. Given information   

The trigonometric function is:

y=-3sin12x

02

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

By comparing given function -3sin12xwith standard sinusoidal functionAsin蝇x

We get amplitudeA=3

Time period isT=2蟺蝇T=2蟺12T=4蟺

So the graph of the given function will have time period 4蟺and amplitude 3

03

Step 3. To find passing points of the graph  

Whenx=0

then y=-3sin12.0y=-3sin0y=-3.0y=0

Graph will pass through (0,0)

when x=蟺

Then

y=-3sin12.蟺y=-3sin蟺2y=-3.1y=-3

So the graph will pass through (0,0) and蟺,-3

Now look at the given graphs from A-D, we can see that

graph (D) has amplitude 3 , time period 4蟺and passing point (0,0) and 蟺,-3

So the graph for given function is graph (D)

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