Question

Determine a coordenada cartesiana (x,y) do ponto em coordenadas polares: (4,-π/3)




Escolha uma:
a. (2,-2√3)
b. (2, 2√3)
c. (-2, √3)
d. (1, 2√3)
e. (5, 2)

Answer 1

$\mathsf{(x,y)=(\rho,\theta)}\\\mathsf{(4,-\dfrac{\pi}{3})=(\rho,\theta)}$

$\mathsf{\rho=4~~\theta=-\dfrac{\pi}{3}}$

$\mathsf{x=\rho.cos(\theta)}\\\mathsf{x=4.cos(-\dfrac{\pi}{3})=4.\dfrac{1}{2}=2}$

$\mathsf{y=4sen(\theta)=4.sen(-\dfrac{\pi}{3})=-2\sqrt{3}}$