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Chapter 7: Q. 94 (page 466)

What are the zeros off(x)=2cos(3x)+1 on the interval [0,2蟺]?

Short Answer

Expert verified

The zeros of the given equation is2蟺9,4蟺9

Step by step solution

01

Step 1. Given Information 

We have to find the zeros off(x)=2cos(3x)+1 on the interval [0,2蟺].

02

Step 2. The zeros are the x values where the graph intersects the x-axis. 

To find the zeros, replace f(x)with 0and solve for x.

Let 3x=y

Now the equation is

0=2cosy+12cosy+1=0

03

Step 3. Subtract 1 on both side 

2cosy+1-1=0-12cosy=-1

Divide by 2 on both side

22cosy=-12cosy=-12

04

Step 4. Solving each equation in the interval [0,2π], we obtain 

y=2蟺3ory=4蟺3

Since y=3x,So

3x=2蟺3or3x=4蟺333x=2蟺3路13or33x=4蟺3路13x=2蟺9orx=4蟺9

So the zeros are2蟺9,4蟺9

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