1. zaphod
2. zaphod

3. satellite73

$$a$$ 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. satellite73

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

5. zaphod

IS THERE ANY OTHER METHOD TO SOLVE IT WITH EQUATIONS.

6. satellite73

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. satellite73

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

8. satellite73

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. zaphod

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

10. satellite73

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

11. satellite73

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

12. zaphod

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

13. satellite73

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. allamiro

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

15. zaphod

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

16. allamiro

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

17. zaphod

cn u show the working @allamiro

18. allamiro

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

19. allamiro

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. zaphod

yes?

21. allamiro

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

22. allamiro

so c = 3

23. zaphod

ok how do u find b now.

24. allamiro

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. zaphod

b?

26. allamiro

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. allamiro

y = 3 when x = 2pi * correctiion

28. allamiro

:)