Homework SourseConsider the point 752 given in rectangular coordinates The
Consider the point (7,5,2) given in rectangular coordinates.
The cylindrical coordinates (r,?,z) of the point are:_________
The spherical coordinates (?,?,? ) of the point are:______________
Next, consider the point (1,(5*pi)/4,6) given in cylindrical coordinates.
The rectangular coordinates of the point are:___________
The spherical coordinates (?,?,? ) of the point are:___________
The cylindrical coordinates (r,?,z) of the point are:_________
The spherical coordinates (?,?,? ) of the point are:______________
Next, consider the point (1,(5*pi)/4,6) given in cylindrical coordinates.
The rectangular coordinates of the point are:___________
The spherical coordinates (?,?,? ) of the point are:___________
Solution
x= r cos t y= r sin t z=z x^2+y^2 = r^2 ==> 49+25 =r^2 ==> r= sqrt(74) (x,y,z)=(7,5,2) ==> z=2 y/x = tant 5/7 = tant ==> t= arctan(5/7) (r,t, z) = (sqrt(74), arctan(5/7), 2) consider the point (1,(5*pi)/4,6) given in cylindrical coordinates. x= 1 cos(pi +pi/4) = -1/ sqrt(2) y= 1 sin(pi +pi/4) = -1/ sqrt(2) z=z ==> z= 6 (x,y,z) = (-1/sqrt(2), -1/sqrt(2), 6)
