Determine the equation of the graph in the form y = acos(bx).
I will try and describe the Graph.
-It starts at the origin (0,0)
-It has a minimum value of -2
-It has a maximum value of 2.
-It has an x-intercept of 90 degrees.
-It starts moving downward below the x-axis, and then curves back upwars, and continues in this pattern.
My answer:
I think "a" should= 2.5, but I do not not what "b" should be. Whatever I put in, I can not get the graph to start at the origin. It always starts above or below y=0.
Could someone please help me?
Thanks.
To determine the equation of the graph in the form y = acos(bx), we can use the given information about the graph:
1. The graph starts at the origin (0,0): This means that when x = 0, y = 0. So, we have the point (0,0) on the graph.
2. The minimum value of y is -2: This tells us that when x = 90 degrees, y = -2. So, we have the point (90, -2) on the graph.
3. The maximum value of y is 2: This tells us that when x = 180 degrees, y = 2. So, we have the point (180, 2) on the graph.
From the given information, we can determine the amplitude (a) and the period (b), which will allow us to determine the equation of the graph.
Amplitude (a):
The amplitude refers to the vertical distance from the midline of the graph to the maximum or minimum point. In this case, we can see that the graph reaches a maximum value of 2 and a minimum value of -2. The amplitude is half of the vertical distance between these two points: (2 - (-2))/2 = 4/2 = 2. Therefore, a = 2.
Period (b):
The period refers to the horizontal distance between two consecutive cycles of the graph. In this case, the x-intercept occurs at 90 degrees. To find the period, we subtract the x-coordinate of the origin (0 degrees) from the x-coordinate of the x-intercept (90 degrees): 90 - 0 = 90. Therefore, the period is 90 degrees.
Now, we can determine the equation of the graph:
y = a*cos(bx)
Substituting the values we found, we have:
y = 2*cos(bx)
The challenge now is to find the value of b that satisfies all the given conditions. Based on the information provided, it seems there might be an error in the given details or the desired equation.
Please provide more information or clarify any discrepancies so that we can assist you better.