Question

Use the inequality 5cos(2x)≤0

5cos⁡⁡(2x)≤0 on [−π,π]

[−π,π] to answer the following questions.

Part A: What are the zeros to the nearest hundredth?

Part B: What is the solution set for the inequality?

Select all correct answers for Part A, and select one answer for Part B. Use π≅3.14

π≅3.14 if needed.

A: x= −1/2π

A: x= −3/4π

A: x= 0π

A: x= −1/4π

A: x= 1/4π

A: x= 3/4π

A: x=−1/2π

B: (−3/4π,−1/4π)∪(1/4π,3/4π)

B: [−1/2π,0π]∪[0π,1/2π]

B: [−1/2π,1/2π]

B: [−3/4π,−1/4π]∪[1/4π,3/4π]

B: (−∞,−3/4π]∪[−1/2π,1/2π]∪[3/4π,∞)

Answer 1

$$5\cos(2x)\leq 0=>\cos(2x)\leq 0$$

If $x\in[-\pi, \pi],$ then $2x\in[-2\pi, 2\pi]$

$$2x\in[-\dfrac{3\pi}{2}, -\dfrac{\pi}{2}]\cup[\dfrac{\pi}{2}, \dfrac{3\pi}{2}]$$

$$x\in[-\dfrac{3\pi}{4}, -\dfrac{\pi}{4}]\cup[\dfrac{\pi}{4}, \dfrac{3\pi}{4}]$$

$$5\cos(2x)= 0$$

$$=>x_1=-\dfrac{3\pi}{4}, x_2=-\dfrac{\pi}{4}, x_3=\dfrac{\pi}{4}, x_4=\dfrac{3\pi}{4}$$

$$=>x_1\approx-2.36, x_2=-0.79, x_3=0.79, x_4=2.36$$

A: x= −3/4π

$\approx-2.36$

A: x= −1/4π

$\approx-0.79$

A: x= 1/4π

$\approx-0.79$

A: x= 3/4π

$\approx2.36$

B: [−3/4π,−1/4π]∪[1/4π,3/4π]