Question

Please help...

Answer 1

http://screencast.com/t/N9H6p6CGYc

Answer 2

@satellite73 @Shadowys @RadEn

Answer 3

\(a\) 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

Answer 4

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

Answer 5

IS THERE ANY OTHER METHOD TO SOLVE IT WITH EQUATIONS.

Answer 6

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 \(b\)

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

that is the entire point of this exercise, not to use equations, but to visualize the period, and amplitude from the picture

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

cn u show the working @allamiro

Answer 18

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

Answer 19

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

Answer 20

yes?

Answer 21

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

Answer 22

so c = 3

Answer 23

ok how do u find b now.

Answer 24

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

Answer 25

b?

Answer 26

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

Answer 27

y = 3 when x = 2pi * correctiion

Answer 28

:)