Chapter 7: Q. 94 (page 466)

What are the zeros of $f (x) = 2 \cos (3 x) + 1$ on the interval $[0, 2 π]$ ?

Short Answer

Expert verified

The zeros of the given equation is $\{\frac{2 π}{9}, \frac{4 π}{9}\}$

Step by step solution

Step 1. Given Information

We have to find the zeros of $f (x) = 2 \cos (3 x) + 1$ 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 $x$ .

Let $3 x = y$

Now the equation is

$0 = 2 \cos y + 1 2 \cos y + 1 = 0$

Step 3. Subtract 1 on both side

$2 \cos y + 1 - 1 = 0 - 1 2 \cos y = - 1$

Divide by 2 on both side

$\frac{2}{2} \cos y = - \frac{1}{2} \cos y = - \frac{1}{2}$

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

$y = \frac{2 π}{3} or y = \frac{4 π}{3}$

Since $y = 3 x$ ,So

$3 x = \frac{2 π}{3} or 3 x = \frac{4 π}{3} \frac{3}{3} x = \frac{2 π}{3} \cdot \frac{1}{3} or \frac{3}{3} x = \frac{4 π}{3} \cdot \frac{1}{3} x = \frac{2 π}{9} or x = \frac{4 π}{9}$

So the zeros are $\{\frac{2 π}{9}, \frac{4 π}{9}\}$

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What are the zeros of $f (x) = 2 \cos (3 x) + 1$ 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. Subtract 1 on both side

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

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What are the zeros off(x)=2cos(3x)+1 on 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. Subtract 1 on both side

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

One App. One Place for Learning.

Most popular questions from this chapter

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What are the zeros of $f (x) = 2 \cos (3 x) + 1$ on the interval $[0, 2 π]$ ?