Math  /  Geometry

QuestionExemple a) Donnez une paramétrisation du cône z=x2+y2z=\sqrt{x^{2}+y^{2}}

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Vérifier que la paramétrisation satisfait l'équation du cône:
z=x2+y2 z = \sqrt{x^2 + y^2} r=(rcos(θ))2+(rsin(θ))2 r = \sqrt{(r \cos(\theta))^2 + (r \sin(\theta))^2} r=r2(cos2(θ)+sin2(θ)) r = \sqrt{r^2 (\cos^2(\theta) + \sin^2(\theta))} r=r2=r r = \sqrt{r^2} = r
La paramétrisation est correcte car elle satisfait l'équation du cône.
La paramétrisation du cône est:
(x(r,θ),y(r,θ),z(r,θ))=(rcos(θ),rsin(θ),r) (x(r, \theta), y(r, \theta), z(r, \theta)) = (r \cos(\theta), r \sin(\theta), r)

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