Question 863222
x = 2sin(t)
y = sin(2t)


as far as i can tell, you eliminate t by solving for t in one of the equations and then using that value of t in the other equation.


your 2 equations are:


x = 2sin(t)
y = sin(2t)


you solve for t in the first equation.
start with:
x = 2sin(t)
divide both sides by 2 to get:
x/2 = sin(t)
this is true if and only if arcsin(x/2) = t
replace t with arcsin(x/2) in the second equation to get:
y = sin(2*arcsin(x/2))
your equations are now in terms of x and f(x).
the equation you can graph is y = sin(2*arcsin(x/2))
finding the domain of this equation can be a challenge.
since the sine of an angle is between -1 and 1, this means that the arcsine of a number is only valid when the number is between -1 and 1.
since the number is x/2, this means that x has to be between -2 and 2 only.  
in order for x to be between -2 and 2 only, this means that t has to be between -pi/2 and pi/2 only.
the graph of your equation is shown below:
<img src = "http://theo.x10hosting.com/2014/apr142.jpg" alt="$$$" </>
the same graph with associated data table created in Excel is shown below:
<img src = "http://theo.x10hosting.com/2014/apr143.jpg" alt="$$$" </>


a decent reference on parametric equations is shown below:
<a href = "http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx" target = "_blank">http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx</a>