Use the graph below of the function to approximate the solutions to $3 \cos ( 2 x ) - \cos ( x ) = 0$ in the interval $[ 0,2 \pi )$. Round your answers to one decimal.

A) 0.7, 2.0, 1.5, 4.8
B) 2.0, 1.5, 4.8, 5.6
C) 2.0, 2.2, 4.0, 5.6
D) 0.7, 2.2, 4.0, 5.6
E) 0.7, 1.5, 4.0, 6.3

Question

Use the graph below of the function to approximate the solutions to $3 \cos ( 2 x ) - \cos ( x ) = 0$ in the interval $[ 0,2 \pi )$. Round your answers to one decimal.

A) 0.7, 2.0, 1.5, 4.8 
B) 2.0, 1.5, 4.8, 5.6 
C) 2.0, 2.2, 4.0, 5.6 
D) 0.7, 2.2, 4.0, 5.6 
E) 0.7, 1.5, 4.0, 6.3

Quizplus · Accepted Answer

We can estimate the solutions by finding the x values where the graph of $y=3 \cos(2x) - \cos(x)$ intersects the x-axis. Using the graph provided, it appears there are four such points in the interval [0, 2π).

- The first intersection occurs between x = 0 and x = 1, and it looks like it is approximately at x = 0.7.
- The second intersection occurs between x = 1 and x = 2, and it looks like it is approximately at x = 2.2.
- The third intersection occurs between x = 3 and x = 4, and it looks like it is approximately at x = 4.0.
- The fourth intersection occurs between x = 5 and x = 6, and it looks like it is approximately at x = 5.6.

Rounding each of these values to one decimal place gives us 0.7, 2.2, 4.0, and 5.6. The only answer choice that includes all of these values is D.

Use the Graph Below of the Function to Approximate the Solutions