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Mathematics
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http://screencast.com/t/N9H6p6CGYc
\(a\) is the amplitude. since this starts and 3 and goes up do 9, then comes back down to 3 and then to -3, the amplitude is 6

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Other answers:

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.
from your eyes you see that the period is \(\pi\) the period of \(\sin(bx)\) is \(\frac{2\pi}{b}\) so set \(\frac{2\pi}{b}=\pi\) and solve for \(b\)
no there are no equations here, you have to visualize, since you are given a picture
well there is an equation to find \(b\) . it is \[\frac{2\pi}{b}=\pi\] but you only know that the period is \(\pi\) from looking at the graph
and i know c, now can i substitute it in the main equation and find a?
that is the entire point of this exercise, not to use equations, but to visualize the period, and amplitude from the picture
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
it is always the case that the period of \(\sin(bx)\) is \(\frac{2\pi}{b}\) we can think of it this way. since is periodic with period \(2\pi\) so it does everything on the interval \([0,2\pi)\) now if \(bx=0\) that means \(x=0\) and if \(bx=2\pi\) that means \(x=\frac{2\pi}{b}\) so that gives you the period
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
cn u show the working @allamiro
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.
yes so now lets say 9 = a sin ( bx) + 3 the highest value for sin when sinx b = 1 so bx = pi /2 so from there a =6
b?
y = 3 when x = pi /2 3 = 6 sin ( b 2 pi ) + 3 6 sin ( 2 b pi) = 0 sin ( 2 b pi ) = sin ( 2b pi ) = sin ( pi ) b = 1/2
y = 3 when x = 2pi * correctiion
:)

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