Question

Eliminate the parameter to find the cartesian equation of the curve: x=7sinθ,y=cos2θ,−π2≤θ≤π2 x=7sin⁡θ,y=cos2⁡θ,−π2≤θ≤π2 the equation of the curve is: y = equation editorequation editor from x = equation editorequation editor to x =

Answer 1

Answer:

$y = 1 - \frac{2}{49}\cdot x^{2}$

Step-by-step explanation:

The parametrical components of the curve are:

$x = 7 \cdot \sin \theta$ and $y = \cos 2\theta$

After some trigonometrical and algebraic handling, the parametrical variable is eliminated in the resulting expression:

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

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

$y = 1 - 2\cdot \left(\frac{x^{2}}{49} \right)$

$y = 1 - \frac{2}{49}\cdot x^{2}$