Finding Trajectory of x & y in Kinematics

[Kitanov]

I need to find a trajectory

x = 4cos(2t) + 3sin(2t)
y = 3cos(2t) - 4sin(2t)

 

[berkeman]

I need to find a trajectory

x = 4cos(2t) + 3sin(2t)
y = 3cos(2t) - 4sin(2t)

To the moon, Alice!

Quiz Question -- what old TV show is that from?

Spoiler

https://www.google.com/search?client=firefox-b-1-d&q=to+the+moon+alice

 

[Baluncore]

I need to find a trajectory

Will it repeat?
How often?

 

[Kitanov]

Will it repeat?
How often?

I don't know what you think will happen again.
That's the whole task, there is no explanation of how the task is done. I can send you where that task is from, but you won't understand anything because it's in Serbian.

http://www.tfzr.uns.ac.rs/Content/files/0/Kinematika - I deo.pdf
Task 2

 

[Baluncore]

The trajectory is a function of 2t.
Sine and cosine repeat evert 2π, so the trajectory will repeat. What period?
Plot values of x and y against t.

 

[Baluncore]

Serbian is easy with google translate...
Page 6 of the .pdf
The question and a solution is presented on that page. I translate, but not all the equations.

Zadatak 2: Kretanje tačke određeno je jednačinama =
Task 2: The motion of a point is determined by equations

𝑥=4cos(2𝑡)+3sin(2𝑡)
𝑦=3cos(2𝑡)−4sin(2𝑡)
(𝑥, 𝑦 - in meters, 𝑡 - in seconds)

Odrediti trajektoriju (putanju), brzinu i ubrzanje tačke u trenutku kada je 𝑡=𝜋[𝑠]
= Determine the trajectory (trajectory), velocity and acceleration of a point at the moment when 𝑡 = 𝜋[𝑠]

Rešenje: = Solution:
Trajektorija (putanja) = Trajectory (path)
Dobijene jednačine kvadrirati i sabrati = Square and add the obtained equations
Brzina = Speed.
Ubrzanje = Acceleration.

 

[Kitanov]

Serbian is easy with google translate...
Page 6 of the .pdf
The question and a solution is presented on that page. I translate, but not all the equations.

Zadatak 2: Kretanje tačke određeno je jednačinama =
Task 2: The motion of a point is determined by equations

𝑥=4cos(2𝑡)+3sin(2𝑡)
𝑦=3cos(2𝑡)−4sin(2𝑡)
(𝑥, 𝑦 - in meters, 𝑡 - in seconds)

Odrediti trajektoriju (putanju), brzinu i ubrzanje tačke u trenutku kada je 𝑡=𝜋[𝑠]
= Determine the trajectory (trajectory), velocity and acceleration of a point at the moment when 𝑡 = 𝜋[𝑠]

Rešenje: = Solution:
Trajektorija (putanja) = Trajectory (path)
Dobijene jednačine kvadrirati i sabrati = Square and add the obtained equations
Brzina = Speed.
Ubrzanje = Acceleration.

I speak Serbian. I understand what is written there, but it was not clear to me why it is done that way.
Now it is.

 

[wrobel]

I need to find a trajectory

x = 4cos(2t) + 3sin(2t)
y = 3cos(2t) - 4sin(2t)

express ##\cos 2t## and ##\sin 2t## and use ##\cos^2+\sin^2=1##