|
Question 1201928: Find a equation in the form y = a sin bx for the following graph.
Point A = (0,0)
Point B = (pi/4, 3)
Point C = (-5pi/4, -3)
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The simplest equation(s) that satisfy the conditions are if the 3 and -3 values are the maximum and minimum values, making the amplitude of the function 3. There might or might not be much more complicated sine functions where the amplitude is greater than 3.
Assuming an amplitude of 3, a is clearly 3.
The function value is 0 at x=0; and it reaches its maximum value of 3 at x=pi/4. The simplest function is then one in which pi/4 is one-fourth of the period; that makes the period pi. So bx has to cover the range from 0 to 2pi as x ranges from 0 to pi; that makes b=2.
ANSWER:
a = 3; b = 2:
y=3sin(2x)
NOTE: The difference in x values between points B and C is 6pi/4 = 3pi/2; with the period being pi, that means it is 1.5 periods between B and C; and since point B is a maximum, point C will be a minimum -- so the graph passes through all three of the given points.
----------------------------------------------------------------
Comment from student: "But what can be a solution for finding a or b?"
!!!!???
My response explains how to find that a is 3 and b is 2...!!!
|
|
|
| |
