Answer to Question #113344 in Calculus for Shane Mulugisi

Question

Eliminate θ from the equations 4x = cos(3θ) + 3 cos θ; 4y = 3 sin θ  sin(3θ)

Answer 1

Eliminate $\theta$ from the equations

$4x=cos(3\theta)+3cos\theta; 4y=3sin\theta-sin(3\theta)$

Solution:

$cos(3\theta)=4cos^3\theta-3cos\theta$

$sin(3\theta)=3in\theta-4cos^3\theta$

$4x=4cos^3\theta-3cos\theta+3cos\theta$

$4y=3sin\theta-3sin\theta+4sin^3\theta$

$x=cos^3\theta$

$y=sin^3\theta$

$x^{\frac{1}{3}}=cos\theta$

$y^{\frac{1}{3}}=sin\theta$

$cos^2\theta+sin^2\theta=1$

Aswer:

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=1.$