Applying trigonometric functions to a problem

[mcof]

Hi,

Can someone show me how to start this problem:

A particle is moving in a plane. The x and y coordinates of the particle are given by
x = sin 48t and y = cos 25t where t is time.
At time t = 0, the particle is at the point (0,1).

How can find all the possible values of t for which the particle is at the origin?

I need help for starting this problem. The rest, maybe I can handle. Thank you.

 

[stapel]

How can find all the possible values of t for which the particle is at the origin?

Solve each function separately for where each equals zero. The intersection (the overlap) of the two sets of answers will be the values of t for which both x and y are zero, and thus the particle is at the origin. :wink:

Eliz.

 

[Deleted member 4993]

Hi,

Can someone show me how to start this problem:

A particle is moving in a plane. The x and y coordinates of the particle are given by
x = sin 48t and y = cos 25t where t is time.
At time t = 0, the particle is at the point (0,1).

How can find all the possible values of t for which the particle is at the origin?

I need help for starting this problem. The rest, maybe I can handle. Thank you.

when does sine function go to 0 -

\(\displaystyle 0, \, \pi, \, 2\pi, \, etc\)

when does cosine function go to 0 -

\(\displaystyle \frac{ \pi}{2}, \, \frac{ 3\pi}{2}, \, \frac{ 5\pi}{2}\, etc\)

so x = 0 at

\(\displaystyle t\,=\, 0\, ,\frac{\pi}{48}\, ,\frac{\pi}{24}\, etc\)

and y = 0 at

\(\displaystyle t\,=\, ,\frac{\pi}{50}\, ,\frac{3\pi}{50}\, etc\)

 

[tkhunny]

First, find one.

x = sin 48t and y = cos 25t where t is time.
At time t = 0, the particle is at the point (0,1).

sin(48(0)) = sin(0) = 0 - OK
cos(25(0)) = cos(0) = 1 - OK

How often does the x-coordinate return to x=0? The period of x = sin(48t) is...
How often does the y-coordinate return to y=1? The period of y = sin(25t) is...
Does it EVER happen at the same time? Th eleasst common multiple of 25 and 48 may give you a clue.

Show us what you get.

 

[mcof]

Thanks a lot for your help!