Parametric Equation to Rectangular Equation

Question

Convert the following parametric equations to a rectangular equation:

           x=2cos²t 

           y=2sin²t      0<t<pi/2

Answer 1

x = 2cos²t

 

y = 2sin²t, 0<t<π/2

 

use the identity: sin²t + cos²t = 1

 

2*(sin²t + cos²t) = 2*1

 

2sin²t + 2cos²t = 2

 

x + y = 2

 

from t = 0 to π/2, the value of x will move from 2cos²(0) = 2 to 2cos²(π/2) = 0

 

the final function will be y = 2 - x| 0 ≤ x ≤ 2.

Answer 2

By rectangular form, I assume you want a function of the type y = f(x).

 

x = 2 cos²t ⇒ cos²t = x/2
y = 2 sin²t = 2(1 - cos²t) = 2(1 - x/2) = 2 - x

 

Therefore the rectangular form is

 

y = 2 - x

 

which is the same as

 

x + y = 2

 

as in Kenneth's answer.

Answer 3

What happens if you add these two equations?  I get x+y = 2