Sketch the parametric curve, is this a valid way of doing it

Question

I've been given the coordinates in vector form of r(t)=(3cos(t))i-(4sin(t))j. Where 0<=t<=2pi

I put 3cos(t) as my x value and -4sin(t) as my y value. For t, i plugged in the values of 0, 1 , pi/2, and 3pi/4. On the x axis, the points are (3,0) and (-3,0). On the y axis, the points are (0,-4) and (0,4). The direction is clockwise.

Is this a valid to sketch the curve?

Answer 1

hint

$$x=3\cos(t)$$

$$y=-4\sin(t)$$

thus

$$\frac{x^2}{9}+\frac{y^2}{16}=1$$

this is an ellipse.