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http://screencast.com/t/N9H6p6CGYc

that is, the range is of length 12 from -3 to 9, so the amplitude is half of that, therefore \(a=6\)

IS THERE ANY OTHER METHOD TO SOLVE IT WITH EQUATIONS.

no there are no equations here, you have to visualize, since you are given a picture

and i know c, now can i substitute it in the main equation and find a?

we know \(c=3\) because this is the graph of sine lifted up 3 units

can u explain why period of sin(bx) = 2pi/b

sub x = pi then x = 2pi when x = pi y =3 when x = 2pi y = 9 then solve the equations

@satellite73 period is for one complete wave right, how come its 2 pi, it has to be pi

when x = 0 y = 0 then solve the equations for a b and c

dsregard the 2 pi thing = 9 just x = pi and x = 0

what you mean show the work x = pi y = 3
3 = a sin ( b* pi ) + c
x= 0 y = 0
0 = a sin ( b * 0 ) + c

yes?

sorry again y = 3 when x = 0 I didnt focus at the graph

so c = 3

ok how do u find b now.

b?

y = 3 when x = 2pi * correctiion

:)