Answer to Question #106870 in Analytic Geometry for khushi

Question #106870
b) Find the cylindrical coordinates of the points where the Cartesian coordinates are (2)
i) (6,6,8)
ii) ( SQRT(2),1,1)
1
Expert's answer
2020-03-30T11:40:58-0400

Transformation "(x,y,z)" to "(\\rho,\\theta,z)"

"\\rho=\\sqrt{x^2+y^2}"

"\\theta=tan^{-1}{\\frac y x}"

"z=z"


i) "\\rho=6\\sqrt{2}"

"\\theta=tan^{-1}1=\\pi\/4"

"z=8"


ii) "\\rho=\\sqrt{2+1}=\\sqrt{3}"

"\\theta=tan^{-1}{{\\frac 1 {\\sqrt2}}}"

"z=1"



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