plot the position vector r(t)= (2cost)i+(3sint)j, such that 0< (or equal to) t< (or equal to) pi (360 degrees)
You need to plug some values of t in the equation of vector to get some position vectors.
I suggest you to select the following values for t: `t = 0, t = pi/2 ; t = pi ; t = 3pi/2.`
`` If t = 0 => x = 2cos 0 = 2; y = 3sin 0 = 0
If `t = pi/2 =gt x = 2cos (pi/2) = 0 ; y = 3 sin(pi/2) = 3`
If `t = pi =gt x = 2cos (pi) = -2; y = 3 sin(pi) = 0`
If `t = 3pi/2 =gt x = 2cos (3pi/2) =0; y = 3 sin(3pi/2) = -3`
Hence, sketching the graph of vector function yields an ellipse whose antipodal points are: (2,0);(-2,0);(0,3) and (0,-3), semi-minor axis b=2 and semi-major axis a=3.