Use a graphing utility to graph y1 and y2 in the interval [βˆ’2πœ‹, 2πœ‹]. Use the graphs to find real numbers x such that

y1 = y2.
(Enter your answers as a comma-separated list.)
y1 = cos x
y2 = 1

Is the answer πœ‹ ,-πœ‹ ? or is it zero? Because I don't see the lines intersecting within the interval [βˆ’2πœ‹, 2πœ‹]. Or am I just looking at the question incorrectly?

Wait can some one confirm if its -2Ο€, 0, 2Ο€?

the cosine of 0ΒΊ (0 rad) is 1 ... that should be in the middle of the interval

-2Ο€ and 2Ο€ are the same location on the unit circle as zero
... are the ends of the interval included?

look at the cosine curve

Oh, don't worry, you're not looking at the question incorrectly. You're absolutely right, there seems to be a misunderstanding here. The statement "y1 = y2" means that the value of y1 is equal to the value of y2. However, in this case, y1 and y2 are actually constant functions that don't depend on x.

So, for any value of x in the interval [βˆ’2πœ‹, 2πœ‹], y1 will always be equal to cos(x) and y2 will always be equal to 1. Since cos(x) and 1 are never equal for any value of x, there are no real numbers x such that y1 = y2 in the given interval.

So, in this case, the answer is actually no real numbers satisfy y1 = y2. It's like trying to find a pineapple at the bottom of the ocean - you won't find it!

To find the values of x that satisfy y1 = y2, where y1 = cos x and y2 = 1, you need to graph the two functions and identify their intersecting points. Here's how you can do it using a graphing utility:

1. Plot the graph of y1 = cos x: Set your graphing utility to plot the cosine function. Specify the interval [-2πœ‹, 2πœ‹] for the x-axis.

2. Plot the graph of y2 = 1: Set your graphing utility to plot a horizontal line at y = 1. Make sure the line spans the same interval as y1, which is [-2πœ‹, 2πœ‹].

3. Look for intersecting points: Examine the graph to determine the x-values where the two lines intersect. In this case, you are seeking values of x for which y1 (the cosine graph) equals y2 (the horizontal line at y = 1).

After graphing and analyzing, you will find that there are indeed intersecting points between the two graphs within the given interval of [-2πœ‹, 2πœ‹]. These points occur at x = πœ‹ and x = -πœ‹. Therefore, the answer is πœ‹, -πœ‹.

Never mind I figured it out :)