Help me

1.  Freq  =  1 / [ 6pi] 

The frequency  is  1 / period....so the period is 6pi....

In the form   y  = Asin (Bx)  + C

Amplitude  = 2  = A

Midline     .....y  = 3    =  C

To find B

B  = 2pi/ period  =   2pi / 6pi   =  1/3

y -intercept  =  (0, 3)

The function is : 

y  = 2sin ( (1/3) x)  + 3

Here's the graph :   https://www.desmos.com/calculator/8hza0yorxy

2.

In the form Asin(Bx)  + C

Amplitude  = 2  = A

Midline  y  = 3  =  C

To find B   =   2pi/ period  =  2pi / 4pi   =  1/2

y intercept  (0, 3)

The function  is :

y  =  2sin( (1/2) x ) + 3

Note  that the parent function is :

y  = -2sin ( (1/2) x )  -  3

Here's the graph of both : https://www.desmos.com/calculator/xnb8aumkek

3.

In the form   y  = Asin (Bx)  + C

Period   =  4     we need to  find "B"  thusly

B  = 2pi / period   = 2pi/ 4  =  pi / 2

A  is the amplitude  =  4

C  is the shift of the midline from y  = 0.....thus.....the shift is 1 unit upward.....so C  = 1

The function is

y  = 4sin (pi * x / 2)  + 1

Here's the graph : 

4.  

y  = Asin(Bx + C )  

A  =  the amplitude  =  [ difference in high/low/point ] / 2  =  6 / 2  =   3

The period is   20sec...so B  =

2pi / period  = 2pi / 20  = pi / 10

Since the sine graph starts at its highest position...the is a shift of pi/2 units to the left....thus  C  = pi/2

The function is :

y = 3sin ((pi/10) x   +  pi/2 )

The only question I have about this one is  at the beginning of the observation, x = 0 and the weight will be at its  highest point......thus.....the graph's first point will not be at the midline......that occurs 5 seconds later.... 

5.

We  have this

y  = Asin (Bx) + C

A is the amplitude  =  5

The midline here is shifted down 8 units from normal.....thus  C  = -8

To find B  we have

B  = 2pi / period    =  2pi / 16  =  pi / 8

So  the function is

y  = 5 sin ( ( pi/ 8)  x )  - 8

Here's the graph :    https://www.desmos.com/calculator/vhovcnbzy3