1. anonymous
2. anonymous

3. anonymous

$$a$$ 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

4. anonymous

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

5. anonymous

IS THERE ANY OTHER METHOD TO SOLVE IT WITH EQUATIONS.

6. anonymous

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 $$b$$

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. anonymous

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

11. anonymous

we know $$c=3$$ because this is the graph of sine lifted up 3 units

12. anonymous

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

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

cn u show the working @allamiro

18. anonymous

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

19. anonymous

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

20. anonymous

yes?

21. anonymous

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

22. anonymous

so c = 3

23. anonymous

ok how do u find b now.

24. anonymous

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

25. anonymous

b?

26. anonymous

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

27. anonymous

y = 3 when x = 2pi * correctiion

28. anonymous

:)