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Консультация № 177743
08.04.2010, 02:01
0.00 руб.
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1
Составить уравнения нормальной плоскости и касательной к кривой в заданной точке.
x=t-sint
y=1-cost
z=2sint
t=пи/4
x=t-sint
y=1-cost
z=2sint
t=пи/4
Обсуждение
Неизвестный
08.04.2010, 04:45
общий
это ответ
Здравствуйте, savelina.
Определим координаты точки касания
x(Pi/4)=Pi/4-[$8730$]2/2
y(Pi/4)=1-[$8730$]2/2
z(Pi/4)=[$8730$]2
x'=1-cos(t)
y'=sin(t)
z'=2*cos(t)
x'(Pi/4)=1-[$8730$]2/2
y'(Pi/4)=[$8730$]2/2
z'(Pi/4)=[$8730$]2
Уравнения касательной в точке t=Pi/4
(x-(Pi/4-[$8730$]2/2))/(1-[$8730$]2/2)=(y-(1-[$8730$]2/2))/([$8730$]2/2)=(z-[$8730$]2)/([$8730$]2)
Уравнение нормальной плоскости в точке t=Pi/4
(1-[$8730$]2/2)*(x-(Pi/4-[$8730$]2/2))+([$8730$]2/2)*(y-(1-[$8730$]2/2))+([$8730$]2)*(z-[$8730$]2)=0
Определим координаты точки касания
x(Pi/4)=Pi/4-[$8730$]2/2
y(Pi/4)=1-[$8730$]2/2
z(Pi/4)=[$8730$]2
x'=1-cos(t)
y'=sin(t)
z'=2*cos(t)
x'(Pi/4)=1-[$8730$]2/2
y'(Pi/4)=[$8730$]2/2
z'(Pi/4)=[$8730$]2
Уравнения касательной в точке t=Pi/4
(x-(Pi/4-[$8730$]2/2))/(1-[$8730$]2/2)=(y-(1-[$8730$]2/2))/([$8730$]2/2)=(z-[$8730$]2)/([$8730$]2)
Уравнение нормальной плоскости в точке t=Pi/4
(1-[$8730$]2/2)*(x-(Pi/4-[$8730$]2/2))+([$8730$]2/2)*(y-(1-[$8730$]2/2))+([$8730$]2)*(z-[$8730$]2)=0
Форма ответа
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