CalculusVolume2-SASG-07-03

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OpenStax Calculus Volume 2 Student Answer and Solution Guide Chapter 7 Parametric Equations and Polar Coordinates 7.3 Polar Coordinates Section Exercises In the following exercises, plot the point whose polar coordinates are given by first constructing the angle and then marking off the distance r along the ray. 125. Answer: 127. Answer:

OpenStax Calculus Volume 2 Student Answer and Solution Guide 129. Answer: 131. Answer:

OpenStax Calculus Volume 2 Student Answer and Solution Guide For the following exercises, consider the polar graph below. Give two sets of polar coordinates for each point. 133. Coordinates of point B . Answer: 135. Coordinates of point D . Answer: For the following exercises, the rectangular coordinates of a point are given. Find two sets of polar coordinates for the point in Round to three decimal places. 137. (3,–4) Answer: 139. Answer:

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OpenStax Calculus Volume 2 Student Answer and Solution Guide 141. Answer: For the following exercises, find rectangular coordinates for the given point in polar coordinates. 143. Answer: 145. Answer: 147. Answer: For the following exercises, determine whether the graphs of the polar equation are symmetric with respect to the -axis, the -axis, or the origin. 149. Answer: Symmetry with respect to the x -axis, y -axis, and origin. 151. Answer: Symmetric with respect to x -axis only. 153. Answer: Symmetry with respect to x -axis only.

OpenStax Calculus Volume 2 Student Answer and Solution Guide For the following exercises, describe the graph of each polar equation. Confirm each description by converting into a rectangular equation. 155. Answer: Line 157. Answer: For the following exercises, convert the rectangular equation to polar form and sketch its graph. 159. Answer: Hyperbola; polar form or For the following exercises, convert the rectangular equation to polar form and sketch its graph. 161. Answer:

OpenStax Calculus Volume 2 Student Answer and Solution Guide

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OpenStax Calculus Volume 2 Student Answer and Solution Guide For the following exercises, convert the polar equation to rectangular form and sketch its graph. 163. Answer: 165. Answer:

OpenStax Calculus Volume 2 Student Answer and Solution Guide For the following exercises, sketch a graph of the polar equation and identify any symmetry. 167. Answer: y -axis symmetry 169. Answer: y -axis symmetry

OpenStax Calculus Volume 2 Student Answer and Solution Guide 171. Answer: x - and y -axis symmetry and symmetry about the pole 173. Answer: x -axis symmetry

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OpenStax Calculus Volume 2 Student Answer and Solution Guide 175. Answer: x - and y -axis symmetry and symmetry about the pole 177. Answer: no symmetry

OpenStax Calculus Volume 2 Student Answer and Solution Guide 179. [T] Use a graphing utility and sketch the graph of Answer: a line 181. [T] Use technology to graph Answer:

OpenStax Calculus Volume 2 Student Answer and Solution Guide 183. Without using technology, sketch the polar curve Answer: 185. [T] Use technology to plot for Answer: 187. [T] Use the results of the preceding two problems to explore the graphs of and for Answer: Answers vary. One possibility is the spiral lines become closer together and the total number of spirals increases.

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CalculusVolume2-SASG-07-03

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