HELP ASAP PLEASE

[blueberry7680]

On the merry-go-round, each horse moves up and down five times in one complete revolution. The up- and - down motion of each horse can be modeled by the function h(t) = 20cos(5ϴ), where h is the horse's displacement in centimetre from its centre and ϴ is the rotation angle of the merry-go-round. Assume the rides begins when ϴ=0 degrees for a given horse.
Answer the following Questions based on the above information:

A) At what rotation angles will the horse be displaced 15 cm above its original position in one revolution?
(B) At what rotation angles will the horse be displaced 10 cm below its original position in one revolution?
(C) How many angles you will get for situation given in part (B).
(D) How long will it take for one complete revolution if the carousel rotates at a speed of 24degrees/sec?
(E) At what rotation angles will the horse be displaced 20 cm below its original position in one revolution?

PLEASE ANSWER WITH THE WHOLE METHOD,THANK YOU

 

[skeeter]

I’d start by graphing the position of the horse for one complete revolution of the merry-go-round to gain a visualization of what’s happening ...

 

[HallsofIvy]

On the merry-go-round, each horse moves up and down five times in one complete revolution. The up- and - down motion of each horse can be modeled by the function h(t) = 20cos(5ϴ), where h is the horse's displacement in centimetre from its centre and ϴ is the rotation angle of the merry-go-round. Assume the rides begins when ϴ=0 degrees for a given horse.
Answer the following Questions based on the above information:

A) At what rotation angles will the horse be displaced 15 cm above its original position in one revolution?

You are told that h(t) = 20cos(5ϴ) so you want to solve
15= 20cos(5ϴ) For what ϴ is cos(5ϴ)= 15/20= 3/4?

(B) At what rotation angles will the horse be displaced 10 cm below its original position in one revolution?

Same as (A) but now you want to solve cos(5ϴ)= 10/20= 1/2.

(C) How many angles you will get for situation given in part (B).

There are, of course, infinitely many values of 5ϴ that satisfy cos(5ϴ)= 1/2. How many ϴ lie between 0 and \(\displaystyle 2\pi\)?

(D) How long will it take for one complete revolution if the carousel rotates at a speed of 24degrees/sec?

There are 360 degrees in a complete rotation so 360/ 24 seconds per rotation.

(E) At what rotation angles will the horse be displaced 20 cm below its original position in one revolution?

This is the same as A and B except that h is now negative.
h(t) = 20cos(5ϴ)= -15. Solve cos(5ϴ)= -15/20= -3/4.

PLEASE ANSWER WITH THE WHOLE METHOD,THANK YOU

If you are not taking a course in which you are taught to solve trig equations, where did you get these problems?

 

[Steven G]

PLEASE ANSWER WITH THE WHOLE METHOD,THANK YOU

Why would I answer your questions for you? This is a math help forum where we help students solve their problems.This is not a job off your homework and come back later to retrieve your answer type forum. If you want help that is great but it will be you, not helpers here, that will solve the problem. We will guide you and give you excellent hints but that is all you should expect from this forum.

 

[blueberry7680]

Why would I answer your questions for you? This is a math help forum where we help students solve their problems.This is not a job off your homework and come back later to retrieve your answer type forum. If you want help that is great but it will be you, not helpers here, that will solve the problem. We will guide you and give you excellent hints but that is all you should expect from this forum.

Not just for you but everyone : Just to clear things up,I am not here to copy the work or cheat,I had problem in the question AND I HAD ALREADY SOLVED IT BEFORE COMING HERE.i had doubts in (B) and (E) part.And more of all I wanted to check my work and the one above whom I have replied through this text I DON'T NEED YOUR HELP AT ALL or I DON'T WANT YOU TO ANSWER MY QUESTION IF YOU DON'T WANT TO hope this clears up.

 

[Dr.Peterson]

Just to clear things up,I am not here to copy the work or cheat,I had problem in the question AND I HAD ALREADY SOLVED IT BEFORE COMING HERE.i had doubts in (B) and (E) part.And more of all I wanted to check my work.

Hi, Blueberry. Please forgive Jomo's rudeness; that is just the way he responds to everyone, not directed at you in particular. But if you had shown work in the first place, and said what you say here rather than "answer with the whole method", then you would have had an answer much sooner!

On the merry-go-round, each horse moves up and down five times in one complete revolution. The up- and - down motion of each horse can be modeled by the function h(t) = 20cos(5ϴ), where h is the horse's displacement in centimetre from its centre and ϴ is the rotation angle of the merry-go-round. Assume the rides begins when ϴ=0 degrees for a given horse.
Answer the following Questions based on the above information:

A) At what rotation angles will the horse be displaced 15 cm above its original position in one revolution?
(B) At what rotation angles will the horse be displaced 10 cm below its original position in one revolution?
(C) How many angles you will get for situation given in part (B).
(D) How long will it take for one complete revolution if the carousel rotates at a speed of 24degrees/sec?
(E) At what rotation angles will the horse be displaced 20 cm below its original position in one revolution?

First, I need to point out that the problem as we have it is stated incorrectly; h(t) = 20cos(5ϴ) should probably be h(ϴ) = 20cos(5ϴ), so that the argument is used in the function! I'll assume that is correct. Also, it is confusing that h(ϴ) is defined as "the horse's displacement in centimetre from its centre", but then they ask about displacement "above its original position", when that would be the top of its motion (due to the use of cosine), not the center. I don't know whether that is intentional, meant to trick you, or a mistake on the author's part. (It seems to have fooled HallsofIvy.)

For part A, you seem (on the surface) to be answering the wrong question. It isn't asking about h(0), but about the angle ϴ at which h(ϴ) = 15. But perhaps you are just observing the point I made about the original position, showing that the original position is at the top. If so, then you did just the right thing (though it should have been explained more fully).

For part B, given that you are taking the problem literally, you have done just right, except for one thing: It asks for "angles ... in one revolution", and you only found one such angle.

I am again confused by part C, as a correct answer to B would include the number of angles! But since you found only one angle, you got that wrong. (See the graph in #2.)

For part D, you are correct.

For part E, I'm not sure what you are saying, but it doesn't seem right.