[SOLVED] Eliminating more trig parameters (sin & cos)

**buddyp450** · January 24th 2010, 06:15 PM

Ok so I thought I'd post this one now that I've been able to work through it a little farther because it didn't quite turn out how I expected graphically...

original problem:

Eliminate the parameter to find a Cartesian equation of the curve
$<br /> x = \frac{1}{2}\cos\theta , y = 2\sin\theta , 0 <= \theta <= \pi<br />$

My steps:

$2x = \cos\theta$ and $\frac{y}{2} = \sin\theta$

1) $2x^2 + \frac{1}{2}y^2 = 1$

2) $\frac{1}{2}y^2 = 1 - 2x^2$

3) $y^2 = 2(1-2x^2)$

4) $y^2 = 2 - 4x^2$

Solution) $y = \sqrt{2-4x^2}$

is this correct? If so how do I graph this appropriately? Do I just graph the function I have for the solution or do I have to plug back in the trigonometric x value?

Thanks

**songoku** · January 24th 2010, 07:31 PM

Originally Posted by buddyp450

1) $2x^2 + \frac{1}{2}y^2 = 1$

This is wrong. Can you figure it out?

And the graph will be an ellipse

**buddyp450** · January 25th 2010, 10:29 AM

solved*

Thread: [SOLVED] Eliminating more trig parameters (sin & cos)

LinkBack

Thread Tools

Display