Explanation Given: a) ( 2 , 3 ) b) ( 4 , − 7 ) c) ( − 3 , − 8 ) d) ( − 5 , 2 ) a) The point ( 2 , 3 ) is in the first quadrant, with x = 2 , y = 3 , Hence θ = tan − 1 ( 3 2 ) ≈ 0.98 Also, r = 2 2 + 3 2 = 13 ≈ 3 .6 Therefore for point ( 2 , 3 ) , ( r , θ ) = ( 3.6 , 0.98 ) b) The point ( 4 , − 7 ) is in the fourth quadrant with x = 4 , y = − 7 , Hence θ = tan − 1 ( − 7 4 ) ≈ − 1.05 Also, r = ( − 7 ) 2 + 4 2 = 65 ≈ 8 .1 Note that tan − 1 an angle less than zero in the fourth quadrant; since we want an angle between 0 and 2 π , we add 2 π to get θ ≈ 2 π − 1.05 ≈ 5.232 Therefore for point ( 4 , − 7 ) , ( r , θ ) = ( 8.1 , 5.2 ) c) The point ( − 3 , − 8 ) is in the third quadrant with x = − 3 , y = − 8 , we have θ = tan − 1 ( − 8 − 3 ) ≈ 1.212 Also, r = ( − 3 ) 2 + ( − 8 ) 2 = 73 ≈ 8 ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

See similar textbooks

Videos

Question

Chapter 12.3, Problem 4E

To determine

To Convert:

Rectangular to polar coordinates using a calculator for:

a) $(2, 3)$

b) $(4, - 7)$

c) $(- 3, - 8)$

d) $(- 5, 2)$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 3E

Chapter 12.3, Problem 5E

Students have asked these similar questions

2 Graph of h 6. The graph of the function h is given in the xy-plane. Which of the following statements is correct? , the graph of h is increasing at an increasing rate. (A) For (B) For (C) For 苏|4 K|4 π π , the graph of h is increasing at a decreasing rate. 2 0 and b>1 (B) a>0 and 01 (D) a<0 and 0

3. Consider the sequences of functions fn: [-T, π] → R, sin(n²x) n(2) n (i) Find a function f : [-T, π] R such that fnf pointwise as n∞. Further, show that f uniformly on [-T,π] as n→ ∞. [20 Marks] (ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7,π]? Justify your answer. [10 Marks]

Good Day, Please assist with the following. Regards,

Chapter 12 Solutions

Calculus - Standalone book

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Rectangular to polar coordinates using a calculator for: a) ( 2 , 3 ) b) ( 4 , − 7 ) c) ( − 3 , − 8 ) d) ( − 5 , 2 )

Solution Summary: The author explains how to convert Rectangular to Polar coordinates using a calculator.

Videos

To Convert:

Rectangular to polar coordinates using a calculator for:

a) $(2, 3)$

b) $(4, - 7)$

c) $(- 3, - 8)$

d) $(- 5, 2)$

Want to see the full answer?

Chapter 12 Solutions

Rectangular to polar coordinates using a calculator for: a) ( 2 , 3 ) b) ( 4 , − 7 ) c) ( − 3 , − 8 ) d) ( − 5 , 2 )

Solution Summary: The author explains how to convert Rectangular to Polar coordinates using a calculator.

Videos

To Convert: Rectangular to polar coordinates using a calculator for: a) (2,3) b) (4,−7) c) (−3,−8) d) (−5,2)

Want to see the full answer?

Chapter 12 Solutions

To Convert:

Rectangular to polar coordinates using a calculator for:

a) $(2, 3)$

b) $(4, - 7)$

c) $(- 3, - 8)$

d) $(- 5, 2)$