Math Bicycle Question HARD STUFF?

Really needed help with this one...

The pedals of a bicycle are mounted on a bracket that is 29.0cm above the ground. Each pedal is 16.5 cm from the bracket. Assume that the bicycle is pedaled at a rate of 12 cycles per minute.
a) Draw a graph showing the height of a pedal above the ground for a few cycles. Assume that the pedal starts at the topmost position at t=0

b) Write an equation for the function in part A
c) Use your equation to determine the heigh of the pedal after 5 seconds, 12 seconds, and 18 seconds

qb
h(t) = 29.0 + 16.5cos (0.4t蟺)

qc
h(5) = 29.0 + 16.5cos (0.4*5*蟺)
= 29 + 16.5cos (2蟺)
= 29 + 16.5*1
= 45.50 cm

h(12) = 29.0 + 16.5cos (0.4*12*蟺)
= 29 + 16.5cos (4.8蟺)
= 29 + 16.5*(-0.809017)
= 15.65 cm

h(18) = 29.0 + 16.5cos (0.4*18*蟺)
= 29 + 16.5cos (7.2蟺)
= 29 + 16.5*(-0.809017)
= 15.65 cm

The motion of the pedals plotted on a graph with the x-axis marked as time will give a Sine wave.

h - final height.
H - height of amplitude of pedals.
Sin - Sine in rad/s.
f - frequency.
t - time of cycle.

Equation:
h = H Sin 2蟺ft

Since you are starting at a maximum height add 蟺/2. Now the equation becomes:

Equation:
h = H Sin (2蟺ft + 蟺/2)

f = 12 cyc./ min.
f = 12 cyc./ 60 sec. (梅 60)
f = 0鈭? cyc. / 1 sec.
f = 0鈭? Hz.

Now the equation becomes:
h = H Sin (2蟺(0鈭?)t + 蟺/2)
h = H Sin (0鈭?蟺t + 蟺/2)

The maximum amplitude of the pedals is 16鈭? cm and the displacement of the height is 29鈭?cm.
So now the equation becomes:
h = H Sin (0鈭?蟺t + 蟺/2)
h = 16鈭? Sin (0鈭?蟺t + 蟺/2) + 29

(a)
Since you are starting at a maximum value draw a Sine wave at it's maximum point (Cosine wave) at t = 0. Remember the curve is displaces by 29cm.
One complete cycle will have a time span of 0鈭? sec.


(b)
h = 16鈭? Sin (0鈭?蟺t + 蟺/2) + 29


(c)
After 5 seconds.
h = 16鈭? Sin (0鈭?蟺t + 蟺/2) + 29
h = 16鈭? Sin (0鈭?蟺(5) + 蟺/2) + 29
h = 16鈭? Sin (5/2 蟺) + 29
h = 16鈭? + 29
h = 45鈭? cm. (For top pedal).
h = 45鈭? - 2(16鈭?)
h = 12鈭? cm (For bottom pedal).


After 12 seconds.
h = 16鈭? Sin (0鈭?蟺t + 蟺/2) + 29
h = 16鈭? Sin (0鈭?蟺(12) + 蟺/2) + 29
h = 16鈭? Sin (5鈭? 蟺) + 29
h = -13鈭?4878... + 29
h = 15鈭?5121... cm. (For top pedal).
The distance the top pedal comes down from the max. height will be the same distance the bottom pedal comes up by.
Height of bottom pedal = Lowest pedal heigth + Max.height - top pedal height.
Height of bottom pedal = 12鈭? + 45鈭? - 15鈭?5121...
Height of bottom pedal = 42鈭?4879...


After 18 seconds.
h = 16鈭? Sin (0鈭?蟺t + 蟺/2) + 29
h = 16鈭? Sin (0鈭?蟺(18) + 蟺/2) + 29
h = 16鈭? Sin (7鈭? 蟺) + 29
h = -13鈭?4878041... + 29
h = 15鈭?5121959... cm. (For top pedal).
Height of bottom pedal = Lowest pedal heigth + Max.height - top pedal height.
Height of bottom pedal = 12鈭? + 45鈭? - 15鈭?5121959......
Height of bottom pedal = 42鈭?48......cm.