Parametric Curve: r(t) = [(sin(4t) / sqrt{2}) - 2]i + [2 sqrt{2} cos(4t) + 1]j

[noobishnoob]

I have no idea what sort of curve this is.

Question 5. The motion of a particle is given by the parametric equations, for \(\displaystyle t\, \in\, \mathbb{R}:\)

. . . . .\(\displaystyle \mathbf{r}(t)\, =\, \left(\dfrac{\sin(4t)}{\sqrt{\strut 2\,}}\, -\, 2\right)\, \mathbf{i}\, +\, \left(2\, \sqrt{\strut 2\,}\, \cos(4t)\, +\, 1\right)\, \mathbf{j}\)

(i) Find the Cartesian equation of the path given by r(t). What type of curve is r(t)?

It definitely is not a circle, so it should be an ellipse, but I'm not really sure either...

 

[Deleted member 4993]

I have no idea what sort of curve this is.

Question 5. The motion of a particle is given by the parametric equations, for \(\displaystyle t\, \in\, \mathbb{R}:\)

. . . . .\(\displaystyle \mathbf{r}(t)\, =\, \left(\dfrac{\sin(4t)}{\sqrt{\strut 2\,}}\, -\, 2\right)\, \mathbf{i}\, +\, \left(2\, \sqrt{\strut 2\,}\, \cos(4t)\, +\, 1\right)\, \mathbf{j}\)

(i) Find the Cartesian equation of the path given by r(t). What type of curve is r(t)?

It definitely is not a circle, so it should be an ellipse, but I'm not really sure either...

r(t) = [sin(4t)/√2 - 2)]i + 4[cos(4t)/√2 + 1/4]j .........continue

 

[noobishnoob]

Question 5. The motion of a particle is given by the parametric equations, for \(\displaystyle t\, \in\, \mathbb{R}:\)

. . . . .\(\displaystyle \mathbf{r}(t)\, =\, \left(\dfrac{\sin(4t)}{\sqrt{\strut 2\,}}\, -\, 2\right)\, \mathbf{i}\, +\, \left(2\, \sqrt{\strut 2\,}\, \cos(4t)\, +\, 1\right)\, \mathbf{j}\)

(i) Find the Cartesian equation of the path given by r(t). What type of curve is r(t)?

r(t) = [sin(4t)/√2 - 2)]i + 4[cos(4t)/√2 + 1/4]j .........continue

Lol im sorry but I dont follow

 

[Ishuda]

I have no idea what sort of curve this is. It definitely is not a circle, so it should be an ellipse, but I'm not really sure either...

Given the form of an ellipse
a (x-x0)^2 + b (y-y0)^2 - c = 0
where a, b, and c are positive, what is an equivalent a, x, x0, b, y, y0 for your problem. What is the squared modulus of r.