Question

Eliminate t from the following parametric equations to find there equivalent Cartesian forms

x=2t cos(t), y=3t sin(t), z = t

Im not sure where to start. If that other multiple of t was not there I would take the the inverse trig function to solve for t. Need a shove in the right direction.

Answer 1

ok, first replace t with z in the equations for x and y

Answer 2

then get and expression for cos(z) and sin(z)

Answer 3

finally use the rule:\[\cos^2(z)+\sin^2(z)=1\]to get rid of the cos/sin.

Answer 4

ok..ill try to work through it

Answer 5

let me know what you find and I'll check it for you.

Answer 6

thank you , ill bb in a min

Answer 7

Ok, im stumped. If I replace z with t I get

x = 2z cos(z) y=3z sin(z)

if I get expressoins for cos and sin

x/2z = cos(z) and y/3z = sin(z)

Im just now sure what good that does?

Answer 8

use the rule I showed you above, i.e.:\[\cos^2(z)+\sin^2(z)=1\]