Question

sketch + describe graph of the curve parametrized by:

x=1-3cos^(2)t
y=-2+4sin^(2)t
-infinity less than t less than infinity

how would i go about solving this.
i know that usually i can solve for t and than plug that in. But for this, i tried using cos^2 + sin^2 = 1... but i'm stuck

Answer 1

cos^2(t)=(1-x)/3
sin^2(t)=(y+2)/4

Add two equations
1=(1-x)/3+(y+2)/4
12=4-4x+3y+6
y=(4/3)x+2/3

Answer 2

i don't really understand parametrized curves. but isn't y=(4/3)x +(2/3) a straight line. So, it doesn't have to be a curve?

Answer 3

Straight line is a special case of the curve just like the natural numbers are a special case of integers