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Chapter 7: Q. 93 (page 466)

What are the zeros off(x)=4sin2x-3on the interval[0,2蟺]?

Short Answer

Expert verified

The zeros of the given equation is蟺3,2蟺3,4蟺3,5蟺3.

Step by step solution

01

Step 1. Given Information

We have to find the zeros off(x)=4sin2x-3on 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.

0=4sin2x-34sin2x-3=0

03

Step 3. Add 3 on both side

4sin2x-3+3=0+34sin2x=3

Divide by 4 on both side

44sin2x=34sin2x=34

04

Step 4. Taking the square root on both side.

sinx=卤34sinx=卤32

Now the factors are

sinx=32orsinx=32

05

Step 5. Solving each equation in the interval [0,2π], we obtain 

x=蟺3,2蟺3orx=4蟺3,5蟺3

So the zeros are蟺3,2蟺3,4蟺3,5蟺3.

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