Chapter 7: Q. 93 (page 466)

What are the zeros of $f (x) = 4 \sin^{2} x - 3$ on the interval $[0, 2 π]$ ?

Short Answer

Expert verified

The zeros of the given equation is $\{\frac{π}{3}, \frac{2 π}{3}, \frac{4 π}{3}, \frac{5 π}{3}\}$ .

Step by step solution

Step 1. Given Information

We have to find the zeros of $f (x) = 4 \sin^{2} x - 3$ on the interval $[0, 2 π]$ .

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

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

$0 = 4 \sin^{2} x - 3 4 \sin^{2} x - 3 = 0$

Step 3. Add 3 on both side

$4 \sin^{2} x - 3 + 3 = 0 + 3 4 \sin^{2} x = 3$

Divide by 4 on both side

$\frac{4}{4} \sin^{2} x = \frac{3}{4} \sin^{2} x = \frac{3}{4}$

Step 4. Taking the square root on both side.

$\sin x = \pm \sqrt{\frac{3}{4}} \sin x = \pm \frac{\sqrt{3}}{2}$

Now the factors are

$\sin x = \frac{\sqrt{3}}{2} or sinx = \frac{\sqrt{3}}{2}$

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

$x = \frac{π}{3}, \frac{2 π}{3} or x = \frac{4 π}{3}, \frac{5 π}{3}$

So the zeros are $\{\frac{π}{3}, \frac{2 π}{3}, \frac{4 π}{3}, \frac{5 π}{3}\}$ .

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What are the zeros of $f (x) = 4 \sin^{2} x - 3$ on the interval $[0, 2 π]$ ?

Short Answer

Step by step solution

Step 1. Given Information

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

Step 3. Add 3 on both side

Step 4. Taking the square root on both side.

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

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

Short Answer

Step by step solution

Step 1. Given Information

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

Step 3. Add 3 on both side

Step 4. Taking the square root on both side.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

What are the zeros of $f (x) = 4 \sin^{2} x - 3$ on the interval $[0, 2 π]$ ?