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Magazine Problem 369
For the following exercises, the rectangular coordinates \((x, y, z)\) of a point are given. Find the cylindrical coordinates \((r, \theta, z)\) of the point. (3,-3,7)
Problem 370
For the following exercises, the rectangular coordinates \((x, y, z)\) of a point are given. Find the cylindrical coordinates \((r, \theta, z)\) of the point. \((-2 \sqrt{2}, 2 \sqrt{2}, 4)\)
Problem 371
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. [T] \(r=4\)
Problem 372
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. [T] \(z=r^{2} \cos ^{2} \theta\)
Problem 373
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. [T] \(r^{2} \cos (2 \theta)+z^{2}+1=0\)
Problem 374
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. [T] \(r=3 \sin \theta\)
Problem 375
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. [T] \(r=2 \cos \theta\)
Problem 376
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. [T] \(r^{2}+z^{2}=5\)
Problem 377
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. [T] \(r=2 \sec \theta\)
Problem 378
For the following exercises, the equation of a surface in cylindrical coordinates is given. Find the equation of the surface in rectangular coordinates. Identify and graph the surface. [T] \(r=3 \csc \theta\)
