Geral
CALCULO-II
Semana 3
0

Questão

Considere o ponto P no espaço tridimensional com coordenadas esféricas (ρ,θ,ϕ)=(2,π4,π3)(ρ,θ,ϕ)=(2,π4,π3)(\rho,\theta,\phi) = \left( 2,\frac{\pi}{4},\frac{\pi}{3} \right). A conversão das coordenadas esféricas para coordenadas retangulares envolve utilizar as relações apropriadas entre (ρ,θ,ϕ)(ρ,θ,ϕ)(\rho,\theta,\phi) e (x,y,z)(x,y,z)(x,y,z).

Neste sentido, assinale a alternativa que indique as coordenadas retangulares do ponto 𝑃.
A) (6√2,6√2,1)(62,62,1)\left( \frac{\sqrt{6}}{2},\frac{\sqrt{6}}{2},1 \right)
B) (1,3–√,−12)(1,3,−12)\left( 1,\sqrt{3}, - \frac{1}{2} \right)
C) (12,2√2,12)(12,22,12)\left( \frac{1}{2},\frac{\sqrt{2}}{2},\frac{1}{2} \right)
D) (3√2,12,3√2)(32,12,32)\left( \frac{\sqrt{3}}{2},\frac{1}{2},\frac{\sqrt{3}}{2} \right)
E) (−1,5–√−32,3√+23)(−1,5−32,3+23)\left( - 1,\sqrt{5} - \frac{3}{2},\frac{\sqrt{3} + 2}{3} \right)
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