#1**+1 **

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

CPhill Feb 8, 2018

#2**+1 **

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

CPhill Feb 8, 2018

#3**+1 **

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 :

CPhill Feb 8, 2018

#4**+1 **

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....

CPhill Feb 8, 2018

#5**+1 **

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

CPhill Feb 8, 2018