Q. 37 In Problems 31鈥�38, plot each p... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 37 (page 567)

In Problems 31鈥�38, plot each point given in polar coordinates $(- 3, - \frac{蟺}{4})$ and find other polar coordinates $(r, 胃)$ of the point for which:
$(a) r > 0, - 2 蟺鈮� 胃 < 0 (b) r < 0, 0 鈮� 胃 < 2 蟺 (c) r > 0, 2 蟺鈮� 胃 < 4 蟺$

Short Answer

Expert verified

The point in the polar coordinate is

Part a. When $r > 0, - 2 蟺鈮� 胃 < 0,$ the other polar coordinates $(r, 胃)$ of the point is $(3, - \frac{5 蟺}{4}) .$

Part b. When $r < 0, 0 鈮� 胃 < 2 蟺,$ the other polar coordinates $(r, 胃)$ of the point is $(- 3, \frac{7 蟺}{4}) .$

Part c. When $r > 0, 2 蟺鈮� 胃 < 4 蟺,$ the other polar coordinates $(r, 胃)$ of the point is $(3, \frac{11 蟺}{4}) .$

Step by step solution

Step 1. Plotting the given points in polar coordinates

The point is $(- 3, - \frac{蟺}{4}) .$ So, $r = - 3 a n d 胃 = - \frac{蟺}{4} .$ As we can see r is negative, the ray will be in the opposite direction of $- \frac{蟺}{4} .$

The point on the polar coordinate is

Part (a) Step 1. Finding the polar coordinates

It is given that $r > 0, - 2 蟺鈮� 胃 < 0 .$ Since $胃$ lies between $- 2 蟺 a n d 0 .$ We have to subtract $蟺$ from the angle $- \frac{蟺}{4}$ to get the polar coordinates.

So, $(3, - \frac{蟺}{4} - 蟺) = (3, - \frac{5 蟺}{4}) .$

Part (b) Step 1. Finding the polar coordinates

It is given that $r < 0, 0 鈮� 胃 < 2 蟺,$ add $2 蟺$ to the angle $- \frac{蟺}{4}$ to get the polar coordinates.

So, $(- 3, - \frac{蟺}{4} + 2 蟺) = (- 3, \frac{7 蟺}{4}) .$

Part (c) Step 1. Finding the polar coordinates

It is given that $r > 0, 2 蟺鈮� 胃 < 4 蟺,$ so rwill be positive and add $3 蟺$ to the angle $- \frac{蟺}{4}$ to get the polar coordinates.

So, $(3, - \frac{蟺}{4} + 3 蟺) = (3, \frac{11 蟺}{4}) .$

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91影视

In Problems 31鈥�38, plot each point given in polar coordinates $(- 3, - \frac{蟺}{4})$ and find other polar coordinates $(r, 胃)$ of the point for which:
$(a) r > 0, - 2 蟺鈮� 胃 < 0 (b) r < 0, 0 鈮� 胃 < 2 蟺 (c) r > 0, 2 蟺鈮� 胃 < 4 蟺$

Short Answer

Step by step solution

Step 1. Plotting the given points in polar coordinates

Part (a) Step 1. Finding the polar coordinates

Part (b) Step 1. Finding the polar coordinates

Part (c) Step 1. Finding the polar coordinates

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91影视

In Problems 31鈥�38, plot each point given in polar coordinates -3,-蟺4and find other polar coordinates r,胃of the point for which:(a)r>0,-2蟺鈮�胃<0(b)r<0,0鈮�胃<2蟺(c)r>0,2蟺鈮�胃<4蟺

Short Answer

Step by step solution

Step 1. Plotting the given points in polar coordinates

Part (a) Step 1. Finding the polar coordinates

Part (b) Step 1. Finding the polar coordinates

Part (c) Step 1. Finding the polar coordinates

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In Problems 31鈥�38, plot each point given in polar coordinates $(- 3, - \frac{蟺}{4})$ and find other polar coordinates $(r, 胃)$ of the point for which:
$(a) r > 0, - 2 蟺鈮� 胃 < 0 (b) r < 0, 0 鈮� 胃 < 2 蟺 (c) r > 0, 2 蟺鈮� 胃 < 4 蟺$