b. Spherical Coordinates: Convert this point to Spherical Coordinates in two ways: C. i. Using https://www.geogebrabrg/classic/PZRQ 27SRZ; Spherical Coordinates GeoGebra applet. Plot the point Orange = (15, 15, 5) and adjust the color accordingly, then adjust the sliders until the red point is in relatively the same place as the orange balloon. You will need to adjust the scaling and the sliders to better t our classroom coordinates. As you do this, be sure to really visualize how each slider affects the location of the point. Write a brief summary of your process and the resulting spherical coordinates below. ii. By hand, showing all work. Give two answers; one using radians and one using degrees. Give exact values when possible. Round approximations to 2 decimal places if needed. Relocation #1: Imagine taking the orange balloon at (15, 15, 5) and pushing it through the oor so that it's equidistant from the xyplane but so that it's now on the other side of the xy- plane. Find the new coordinates of the orange balloon in all 3 coordinate systems using radians for angles. Give exact values when possible, or round to 2 decimals when needed. i. Rectangular ii. Cylindrical iii. Spherical Exercise A (12 pts): We will now explore cylindrical and spherical coordinates using our balloons: Balloons in the Virtual Classroom: httns:lfwww.geogebra.org/classic/ppvagws .Blue=(10, 3, 3) .Red=(2, 22, 4) OYellow=(21,21,7) O Orange = (15, 15, 5) 0 Green = (25, 16, 1) . Purple = (23, 2, 5) 1. Points: Consider the orange balloon at (15, 15, 5). a. Cylindrical Coordinates: Convert this point to Cylindrical Coordinates in two ways: i. Using https://www.geogebra.org/classic/X3j2821((3; Cylindrical Coordinates GeoGebra applet. Plot the point Orange = (15, 15, 5) and adjust the color accordingly, then adjust the sliders until the red point is in relatively the same place as the orange balloon. You will need to adjust the scaling and the sliders to better t our classroom coordinates. As you do this, be sure to really visualize how each slider affects the location of the point. Write a brief summary of your process and the resulting cylindrical coordinates below. ii. By hand, showing all work. Give two answers; one using radians and one using degrees. Give exact values when possible. Round approximations to 2 decimal places if needed. d. Relocation #2: Imagine taking the orange balloon at (15, 15, 5) and pushing it through the white board so that it's equidistant from the yzplane but so that it's now on the other side of the yz-plane. Find the new coordinates of the orange balloon in all 3 coordinate systems using radians for angles. Give exact values when possible, or round to 2 decimals when needed. i. Rectangular ii. Cylindrical iii. Spherical Page 2 of4 2. Spheres: Consider a sphere centered at the origin through the green balloon. Find an equation of this sphere in all 3 coordinate systems, trying to make each equation as simple as possible. a C. . Rectangular Equation b. Cylindrical Equation Spherical Equation d. Check your answer to (a) in GeoGebra by typing in the Rectangular Equation. Does it create a sphere centered at the origin through the green balloon? 3. Cylinders: Consider a cylinder centered at the origin through the red balloon. Find an equation of this cylinder in all 3 coordinate systems, trying to make each equation as simple as possible. a. Rectangular Equation b. Cylindrical Equation 0. Spherical Equation d. Check your answer to (a) in GeoGebra by typing in the Rectangular Equation. Does it create a cylinder centered at the origin through the red balloon
