Question

A sine function has maximum value at (5,-1). The next minimum to the right is at (13, -8). What is the equation of the function

Answer 1

the equation of the centre of the curve is found by the average of the y values

y = -1 and y = -8 so (-1 + (-8)) = -4.5 whhich is halfway between the max and min

so the equation is y = sin(ax) - 4.5

Answer 2

what about the period and phase shift?

Answer 3

the amplitude is 3.5 so its y = 3.5sin(ax + b) - 4.5

Answer 4

i know how to get the amp how do you get the period and phase shift?

Answer 5

well there is a zero at x (9, -4.5). If you know the max and min, differentiate the function and let the derivative = 0 then solve is a method

Answer 6

the phase shift is -1 the curve moves to the right of the y axis 1 unit.... th reasoning is the distance between max and min is 8 units.... so the curve starts 4 units to the left of x = 5 and finishes at x = 17, 4 units to the right of the min...

Answer 7

the period is 16 units, which is double the distance between max and min

Answer 8

so the answer is : 3.5sin2pie(x-1)/16-4.5 ??

Answer 9

right??

Answer 10

yep... thats it... I just graphed it

Answer 11

thats a tough question