1. zaphod Group Title
2. zaphod Group Title

3. satellite73 Group Title

$$a$$ 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 Group Title

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

5. zaphod Group Title

IS THERE ANY OTHER METHOD TO SOLVE IT WITH EQUATIONS.

6. satellite73 Group Title

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 Group Title

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

8. satellite73 Group Title

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 Group Title

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

10. satellite73 Group Title

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

11. satellite73 Group Title

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

12. zaphod Group Title

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

13. satellite73 Group Title

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 Group Title

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

15. zaphod Group Title

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

16. allamiro Group Title

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

17. zaphod Group Title

cn u show the working @allamiro

18. allamiro Group Title

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

19. allamiro Group Title

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 Group Title

yes?

21. allamiro Group Title

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

22. allamiro Group Title

so c = 3

23. zaphod Group Title

ok how do u find b now.

24. allamiro Group Title

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 Group Title

b?

26. allamiro Group Title

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 Group Title

y = 3 when x = 2pi * correctiion

28. allamiro Group Title

:)