Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval square bracket0, 2π)
sin 2x + 1.5 cos x = 0
a. x = 1.624, 1.932, 5.776, 5.997
b. x = 1.055, 3.785, 4.652, 5.721
c. x = 1.101, 2.118, 3.982, 5.104
d. x = 1.484, 13799, 4.626, 5.490
e. x = 1.571, 3.990, 4.712, 5.435
so, did you do it?
what did you get?
try wolframalpha.com
http://www.wolframalpha.com/input/?i=sin+2x+%2B+1.5+cos+x,+0%3Cx%3C2pi
To approximate the solutions to the equation sin 2x + 1.5 cos x = 0 using a graphing utility, you can follow these steps:
1. Open a graphing utility, such as Desmos or GeoGebra, on your computer or smartphone.
2. Enter the equation sin 2x + 1.5 cos x = 0 into the graphing utility's equation input.
3. Set the graphing window to the interval [0, 2π). This will ensure that you only see the solutions within this interval.
4. Plot the graph of the equation by choosing the "Graph" or "Plot" button in the graphing utility.
5. Analyze the graph to identify the x-values where the graph intersects or closely approaches the x-axis. These points correspond to the solutions of the equation.
6. Using the graphing utility's zooming or panning tools, zoom in or navigate the graph to get a more precise estimation of the solutions.
7. Once you have a clear view of the points where the graph intersects or closely approaches the x-axis, read the x-values from the graph.
8. Approximate the x-values to three decimal places.
Comparing the given answer choices with the solutions obtained from the graphing utility, it appears that the correct option is:
e. x = 1.571, 3.990, 4.712, 5.435
Note that the exact values of the solutions may not be represented exactly in the given answer choices, but the decimals provided are the closest approximations within the interval [0, 2π).