Solve for Path of Particle: x - 2cos(arcsin(y/2)) = 0

[Kaura]

Homework Statement

Suppose that a particle follows the path
r(t) = 2cos(t)i + 2sin(t)j
Give an equation (in the form of a formula involving x and y set equal to 0 ) whose whose solutions consist of the path of the particle.

Homework Equations

None that come to mind

The Attempt at a Solution

I set x = 2cos(t) and y = 2sin(t)
thus t = arcsin(y/2)
then x = 2cos(arcsin(y/2))
then x - 2cos(arcsin(y/2)) = 0

It says that this is wrong
I am not all to familiar with doing this type of problem though I suspect that the inverse trigonometric could be messing up the domain of the solution

This is the last problem I need for the homework so any help would be much appreciated

 

[LCKurtz]

Homework Statement

Suppose that a particle follows the path
r(t) = 2cos(t)i + 2sin(t)j
Give an equation (in the form of a formula involving x and y set equal to 0 ) whose whose solutions consist of the path of the particle.

Homework Equations

None that come to mind

The Attempt at a Solution

I set x = 2cos(t) and y = 2sin(t)

This is the last problem I need for the homework so any help would be much appreciated

Try squaring $x$ and $y$ and see if anything comes to mind.

 

[BvU]

Can you draw a few points of the path ? Take easy values for $t$, like ${\pi\over 6},\ {\pi \over 4},\ {\pi\over 3}\$ etc.

 

[Kaura]

Alright I finally got it
r(t) = 2cos(t)i + 2sin(t)j
x = 2cos(t)
y = 2sin(t)
x^2 = 4cos^2(t)
y^2 = 4sin^2(t)
x^2+y^2=4
x^2+y^2-4=0
This answer was accepted as correct
I did not even think about squaring the variables thanks

 

[Ray Vickson]

Alright I finally got it
r(t) = 2cos(t)i + 2sin(t)j
x = 2cos(t)
y = 2sin(t)
x^2 = 4cos^2(t)
y^2 = 4sin^2(t)
x^2+y^2=4
x^2+y^2-4=0
This answer was accepted as correct
I did not even think about squaring the variables thanks

Whenever you see $\sin(at)$ and $\cos(at)$ appearing together in some equation or parametrization, you should always look at what happens when you square them. Sometimes squaring will not work, but sometimes it solve a problem very easily---all you can do is try it and see.