Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval [0, 2π).
A)x = 1.624, 1.932, 5.776, 5.997
B)x = 1.101, 2.118, 3.982, 5.104
C)x = 1.571, 3.990, 4.712, 5.435
D)x = 1.055, 3.785, 4.652, 5.721
E)x = 1.484, 3.799, 4.626, 5.490

Question

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval [0, 2π). ​  ​
A)x = 1.624, 1.932, 5.776, 5.997 
B)​x = 1.101, 2.118, 3.982, 5.104 
C)​x = 1.571, 3.990, 4.712, 5.435 
D)​x = 1.055, 3.785, 4.652, 5.721 
E)​x = 1.484, 3.799, 4.626, 5.490

Quizplus · Accepted Answer

Using a graphing utility to graph ​y = 2cos(x) - 3sin(x), we obtain:

graph

From the graph, we can see that there are four solutions in the interval [0, 2π), which are approximately x = 1.571, 3.990, 4.712, and 5.435. These correspond to the four points of intersection between the graph of y = 2cos(x) - 3sin(x) and the x-axis.

Therefore, the best choice is C.

Use a Graphing Utility to Approximate the Solutions (To Three