## anonymous one year ago write the equation of the function represented by the following graph medal

1. anonymous

2. jim_thompson5910

See if you can determine * The amplitude * The period

3. anonymous

3 and pi/4

4. jim_thompson5910

The period is actually pi/2

5. jim_thompson5910

But you have the right amplitude

6. anonymous

got it then what next

7. jim_thompson5910

The y-intercept is not 0, and the relative extrema is at the y-intercept, so we have a cosine function here Since the y-intercept is negative, this means that the cosine function has a negative coefficient

8. jim_thompson5910

General form y = A*cos(Bx-C)+D C = 0 and D = 0, so don't worry about those |A| = amplitude T = 2pi/B is the period

9. jim_thompson5910

with T = 2pi/B you can solve for B to get B = 2pi/T plug in the period T=pi/2 and simplify

10. anonymous

b=0 and t=0? @jim_thompson5910

11. jim_thompson5910

T = pi/2 is the period its not t = 0

12. jim_thompson5910

$\Large B = \frac{2\pi}{T}$ $\Large B = \frac{2\pi}{\pi/2}$ $\Large B = ??$

13. anonymous

b= 90 degrees

14. jim_thompson5910

idk how you're getting that

15. anonymous
16. anonymous

0

17. jim_thompson5910

can you simplify this expression? $\Large \frac{2\pi}{\pi/2}$

18. anonymous

1

19. jim_thompson5910

not quite

20. jim_thompson5910

$\Large \frac{2\pi}{\pi/2} = \frac{2\pi}{1} \times \frac{2}{\pi} = ???$

21. anonymous

0

22. anonymous

@jim_thompson5910

23. jim_thompson5910

no, forget about the pi think of the pi as x if you have to

24. jim_thompson5910

2x/1 times 2/x simplifies to what?

25. anonymous

4

26. jim_thompson5910

so B = 4

27. jim_thompson5910

what is A?

28. anonymous

1

29. jim_thompson5910

no, remember that above I said that |A| = amplitude and you said earlier that the amplitude was 3

30. anonymous

sorry it 3

31. jim_thompson5910

it's actually -3 to make sure that the y-intercept is -3

32. jim_thompson5910

so A = -3 B = 4

33. jim_thompson5910

y = A*cos(Bx-C)+D A = -3 B = 4 C = 0 D = 0

34. anonymous

so its y=-3cos(4x):)

35. anonymous

36. jim_thompson5910

yes correct

37. anonymous

thanks so much !!!