Find polar coordinates of all points at which the polar curve has ahorizontal or a vertical tangent line. r = a sin(0).-1.0-0.5201.51.00.50.51.0(8 from 0 to 27)

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Answered: Find polar coordinates of all points at…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Find the points at which the following polar curve has a horizontal or a vertical tangent line. r=9-9 sin 0 Identify the points where the curve has a horizontal tangent line. Select all that apply. U A. G. A. D. 27 11 2 6 G. 27 7π 2 27 π 6 27 T 2 ~~ 27 5 2 " B. 18, 3л 18,- H. B. Identify the points where the curve has a vertical tangent line. Select all that apply. E. 18, H. 3π 2 9 5 18. BN ~|~ EN 27 7л " E | 0 " 6 11T C. 6 F. 1. C. ד ☐I. π |N 2'6 π 27 5π 2 6 OIN FIN NI 5п 2'6 (9)
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Find the length of the polar curve. r= sine, 0<0SI Solve by hand. No calculator. Show all work.
Find the points at which the following polar curve has a horizontal or a vertical tangent line. r=2 sin 20 At what points does the polar curve have a horizontal tangent line? OA. (0.2). (0.). (2,0,), and (±2,7 +0₁), where tan 0₁ = √/2 4√/2 4√2 + 3-0₁, where tan 0₁ = √2 OB. (0,0), (0,r), 3x 4√2 O C. 1 (0.). (0.²). (+41² 0₁). and (+4+²,2-0,), where tand, = -√2 4√2) (* 3 3-0₂ √√2 4√3 OD. (0,0), (0,r), , and and t 4√3 -0₁ , where tan 0₁ = √3 At what points does the polar curve have a vertical tangent line? ○ D. (0,0), (0,2), ( + 4√2,0₂), and (± 1 O A. (0,0), (0,), (±2,0₂), and (±2,x+0₂), where tan 8₂ = √√2 4√2 4√2 1 OB. t --0₂ 3 (0.5) - (0.-27). (+44² 0₂2). and (+44² 4-83). Where tan 02 and (2 - 4√³ x-₂): O C. (0.7), (0.37). (+ 4√³,0₂), 3 , where tan 0₂ = 4√/2 3-02, where tan 0₂ = √2 1 √√3
12 and your points should be visible on the graph. Use the polar grid provided. Find the tangents at the pole for this curve and add them to your graph. (a) Graph the rose curve r = 5 sin(30). Your work should include a table of values in multiples of T/2 5Tt/12 Tt/3 7Tt/12 T/A 2Tt/3 5T/ 4 Tt/12 T/6 9/1l 23Tt/12 9/219 11TT/12 137t/12
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Find polar coordinates of all points at which the polar curve has a horizontal or a vertical tangent line. r = a sin(0). -1.0 -0.5 20 1.5 1.0 0.5 0.5 1.0 (8 from 0 to 2 TT)