Question

Rectangular equation for the curve whose parametric equations are x = 2cosθ, y = cos2θ.

Answer 1

The rectangular equation for the curve is $y = \frac{x^{2}}{2} -1$.

In this question, we have a set of parametric equation which must be reduced into a single rectangular equation both by algebraic and trigonometric means, that is to say:

$x = f(\theta), y = g(\theta) \to y = h(x)$

If we know that $x = 2\cdot \cos \theta$ and $y = \cos 2\theta$, then the rectangular equation is:

$y = \cos 2\theta$

$y = \cos^{2}\theta - \sin^{2}\theta$

$y = 2\cdot \cos^{2}\theta -1$

$\cos \theta = \frac{x}{2}$

$y = 2\cdot \left(\frac{x}{2} \right)^{2}-1$

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

The rectangular equation for the curve is $y = \frac{x^{2}}{2} -1$.

We kindly invite to check this question on parametric equations: brainly.com/question/23070611