SOLUTION: 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)

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...!!!

RELATED QUESTIONS
a quadratic graph has maximum point (2,5) and passes through point (0,-3). Find the... (answered by Fombitz)

Find the solutions 18cot2x - 6 = 0 in the interval from 0 to two pi inclusive. a) pi/3,... (answered by lwsshak3)

What values for, theta(0<=theta<=2pi) satisfy the equation? tan^2 theta=-3/2 sec theta (answered by stanbon)

Find all values of x that satisfy the equation 2cosx-1=0, in the interval [0, 2pi] The (answered by ikleyn,MathLover1)

A parabola with an equation of the form y = ax^2 + bx + c has the point (-2, 1) as its... (answered by Fombitz)

Create the quadratic equation in the form y=ax^2+bx+c using the point (0,4)as one point... (answered by Fombitz)

Find an equation of the tangent line to the following graph at the given point... (answered by robertb)

1. Use table of values and plotting points in polar grid to graph the polar equation... (answered by Theo)

What values are for (theta)(0 less than or equal to theta pi) satisfy the equation? a) (answered by Edwin McCravy)