Rectangular-to-Polar Conversion In Exercises 33-40, plot the point given in rectangular coordinates and find two sets of polar coordinates for the point for 0 ≤ 0 < 2π. 35. (1, 1)
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- Find the polar coordinates (r, θ ) of the point whose rectangular coordinates are (x,y) = (-4,4). Show your work.Find a set of parametric equations for the line passing through the point (2, 0, 5) that is parallel to the plane given by x + y + z = 5, and perpendicular to the line x = −1 + t, y = 1 + t, z = 6 − t. (Enter your answers as a comma-separated list.)Determine whether the statement, "When converting a point from polar coordinates to rectangular coordinates, there are infinitely many possiblerectangular coordinate pairs." makes sense or does not make sense, and explain your reasoning.
- How do you know the region in polar coordinates? How to find the polar coordinates?Find a set of parametric equations of the line with the given characteristics. The line passes through the point (2, 3, 4) and is perpendicular to the plane given by 3x + 2y − z = 6.Find polar coordinates (r, θ) of the point (1, −2), where r > 0 and 0 ≤ θ < 2π.
- Find a set of parametric equations of the line with the given characteristics. The line passes through the point (−6, 0, 8) and is parallel to the line x = 5 − 2t, y = −4 + 2t, z = 02. Find the general relation between cartesian and polar coordinatesFind the parametric equations of the intersection of the planes x + (y − 9) + z = 0 and −x + (y + 9) − z = 0. Use the parameter t. Enter your answers as a comma-separated list of equations.)
- Find the polar coordinates ( r , θ ) of a point with Cartesian coordinates ( x , y ) = ( 5 square root 3 / 2, - 5 / 2 )Find a set of parametric equations of the line with the given characteristics. The line passes through the point (1, 2, 3) and is parallel to the line given by x = y = z.Describe the test for symmetry with respect to the polar axis.