Sarah Word Problem

Make the equation (I am not sure if I rember all the detales exactly for this one , I am also not sure if it starts at zero , so if u can show mw what wouldt be the differance if it starts at zero or not)
A water flow reaches a min of 20 m and a max of 30 m , it takes it 6.2 hours to complete a full cycle it starts when t=0. write a sine and a cosine function to model the wave.
b) how long does it take to reach 28 m?





Range 30-20 is 10 so the amplitude is 5

Period is 6.2

Frequency is 2pi/6.2

Beginning point (0, 25)

y=____sin(____x+____)+____

y=5 sin(2pi/6.2 x ) +25

y=5 cos(2pi/6.2 x - pi/2) +25

To make it cos you need a phase shift of right of pi/2 (this is always true to go between sin and cos it doesn't matter what the numbers are)

To reach 28 m

Plug in 28 for y

28 = y=5 sin(2pi/6.2 x ) +25

subtract 25

3 = 5 sin(2pi/6.2 x )

divide by 5

0.6 = sin(2pi/6.2 x )

sin inverse of (0.6) = 2pi/6.2 x

.64 = 2pi/6.2 x

x = .63

So a little over half an hour.

YOU CAN SEE THIS ON THE GRAPH ABOVE

The final problem that I remember is
A wheel has a diameter of 70 and it is spins at 30 km/h
what is the angular velocity in m/s?