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Chapter 5: Problem 75

Use a graphing utility to approximate the solutions of the equation in the interval \([0,2 \pi)\). $$\cos \left(x+\frac{\pi}{4}\right)+\cos \left(x-\frac{\pi}{4}\right)=1$$

Short Answer

Expert verified
The solutions can be estimated from the graph where it intersects with the x-axis. The precise values will depend on the accuracy of the graphing calculator.

Step by step solution

01

Format the Equation

Ensure that the equation is properly formatted to be inputted into the graphing calculator. It should look something like this: \( cos(x+ \frac{\pi}{4}) + cos(x-\frac{\pi}{4})=1 \)
02

Set the Interval

The interval for the solutions is from 0 to \(2 \pi\). Set this range on the x-axis of the graphing tool to limit the solutions within this interval.
03

Plot the Graph

After inputting the equation and setting the interval, plot the graph to visualize the equation within the interval.
04

Approximate the solution

Now, identify the x coordinates of the points where the graph intersects the x-axis. These are the solutions to the equation within the given interval.

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