How do I convert this parametric equation to its rectangular equation? X=4sin3t Y=cos3t

Answer 1

x=4sin3t, y=cos3t

x/4=sin3t

y=cos3t

(x/4)^2=(sin3t)^2

y^2=(cos3t)^2

(x^2/16)=(sin3t)^2

y^2=(cos3t)^2

add the two equations

(x^2/16)+y^2=(sin3t)^2+(cos3t)^2

the angles for sin and cos are the same, 3t

use the trig identity sin^2(3t)+cos^2(3t)=1 (because again the angles , 3t, are the same)

(x^2/16)+y^2=1

multiply both sides by 16

x^2+16y^2=16 is the equation