Question

Find a Cartesian equation for the curvegiven in parametric form byx(t) = 4 cos2t , y(t) = 3 sin2t .

Answer 1

I think eliminating t from those two equations will do.

Answer 2

no more complicated...@ experimentx...

Answer 3

well the straightforward way is solve x(t) for 2t and substitute it in for 2t in y(t)
\[2t = \cos^{-1} (x/4)\]
\[y = 3\sin (\cos^{-1} (x/4)) = 3\sqrt{1-\cos^{2} (\cos^{-1} (x/4))}\]
\[y = 3\sqrt{1-\frac{x^{2}}{16}}\]

Answer 4

x = 4 cos2t
x/4 = cos2t
(x/4)^2 = (cos2t)^2 ---- 1

y = 3 sin2t
y/3 = sin2t
(y/3)^2 = (sin2t)^2 -----2

add 1 and 2

(y/3)^2+(x/4)^2 = (sin2t)^2 + (cos2t)^2 = 1

(y/3)^2+(x/4)^2 = 1
An ellipse.

Answer 5

well according to the answer choices 1.. 4x + 3 y = 12
2.x/4 -y/3=1/12
. 3x − 4 y = 12

Answer 6

lemme type the other ones

Answer 7

@experimentX, thats the better or more efficient way of doing it :)

Answer 8

4.x/3-y/4=1/12
5.3x + 4 y = 12
6.x/3+4y=12

Answer 9

thanks ... learned on OS. and your's is my classic and always working one.

Answer 10

torken, none of the choices have x or y squared ??

Answer 11

nope

Answer 12

its def not a linear equation

Answer 13

hmm

Answer 14

http://www.wolframalpha.com/input/?i=plot+x%28t%29+%3D+4+cos2t+%2C+y%28t%29+%3D+3+sin2t

Answer 15

x(t)=4cos^2 2t y(t)=3sin^2 2t

Answer 16

i forgot to put the cos^2 and sin ^2 >.<

Answer 17

bad luck ... just add them, you will have lines.

Answer 18

haha

Answer 19

x/4 + y/3 = 1

3x +4y = 12

Answer 20

thx much hehe sooo confusing questions ><