Trig Word problem using asin(bx+c)+d

[Louise Johnson]

I have been working through this word problem and could use some help especially with questions c and d
Thank you
Louise

Question: The pedals on a bicycle have a minimum height above the ground of 28cm and a minimum distance of 6cm above ground. A cyclist is pedalling at a constant rate of 15 cycles per minute.

A) What is the period of this periodic function?
Answer 4seconds

B) Write a sine equation for this function assuming that at time t=0 the pedal is at its minimum.
Answer 11sin(24x+3pi/2)+17

C) How high above the ground is the pedal after 4.75 seconds?

Answer 11.5cm

D) Determine a time within the first cycle when the pedal is 25cm above the ground. (give answer to two decimal points).
Answer 2.71 seconds

 

[wjm11]

Question: The pedals on a bicycle have a minimum height above the ground of 28cm and a minimum distance of 6cm above ground. A cyclist is pedalling at a constant rate of 15 cycles per minute.

A) What is the period of this periodic function?
Answer 4seconds

B) Write a sine equation for this function assuming that at time t=0 the pedal is at its minimum.
Answer 11sin(24x+3pi/2)+17

First, I’ll assume you meant the maximum height above the ground is 28cm.

You have correctly calculated the period (4s), amplitude (11), and vertical displacement (17) of the function.

Where did the (24x+3pi/2) come from? The coefficient of x will be 2pi divided by the period. The unaltered sine function has a period of 2pi. In this problem, that would be altered to 4 by making the coefficient of x equal to 2pi/4 = pi/2.

The second term (where you wrote 3pi/2) adjusts for the phase shift (or horizontal displacement), which in this case is 1/4 of a period (4s) to the right or ¾ of a period to the left, since at t=0, the pedal is at its minimum.

Y = 17 + 11sin(pi/2(x – 1)) where y is the height and x is the time in seconds.

For c) just plug in the time value for x and solve for y.

For d) just plug the height value in for y and solve for x.

 

[Louise Johnson]

Hello WJM11,
Thank you for your help, I was getting worried that no one was going to reply!. I have gone over this a few more times and can see where I went wrong.
I did what you suggested and plugged in the numbers and solved for x and y. (late nights let me tell you!! )

Thank you again

Louise

 

[wjm11]

With the corrected equation, the answers for c and d are:

c) 12.79 cm

d) 1.52s or 2.48s