Please solve this calc problem please Please label each part of your solution with the corresponding A, B, C.Consider the curve defined as r = 6 sin(40)A. Find all angles, 0, such that r = 0 for 0 ≤ 0 ≤ TB. Set up an integral which represents the area of one petal of this rose. (Hint: You will need your work from Part A for this question)C. What is the area of one petal of this rose? (Your answer must be exact. If you type it into a calculator and get a decimal, then your answer is not exact.)

Let us consider the polar curve, .(a)Find the all values of such that .Further,It implies that the…

Answered: Please label each part of your solution…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Please solve this calc problem please

Please label each part of your solution with the corresponding A, B, C.
Consider the curve defined as r = 6 sin(40)
A. Find all angles, 0, such that r = 0 for 0 ≤ 0 ≤ T
B. Set up an integral which represents the area of one petal of this rose. (Hint: You will need your work from Part A for this question)
C. What is the area of one petal of this rose? (Your answer must be exact. If you type it into a calculator and get a decimal, then your answer is not exact.)

Expert Solution

Step 1: Solutions

Let us consider the polar curve, $r equals 6 sin left parenthesis 4 theta right parenthesis comma space w h e r e space 0 less or equal than theta less or equal than pi$ .

(a)

Find the all values of $theta$ such that $r equals 0$ .

Further,

$table row cell 6 sin left parenthesis 4 theta right parenthesis end cell equals 0 row cell sin left parenthesis 4 theta right parenthesis end cell equals 0 row cell 4 theta end cell equals cell n pi space space space space space.... left parenthesis sin left parenthesis theta right parenthesis equals 0 rightwards double arrow theta equals n pi comma space n element of straight integer numbers end cell row theta equals cell fraction numerator left parenthesis n pi right parenthesis over denominator 4 end fraction comma space n element of straight integer numbers end cell row blank rightwards double arrow cell theta equals 0 comma space straight pi over 4 comma straight pi over 2 comma space fraction numerator 3 straight pi over denominator 4 end fraction space element of left square bracket 0 comma space straight pi right square bracket end cell end table$

It implies that the values of angle $theta$ are $theta equals table row blank blank 0 end table table row blank blank comma end table table row blank blank space end table table row blank blank cell straight pi over 4 end cell end table table row blank blank comma end table table row blank blank cell straight pi over 2 end cell end table table row blank blank comma end table table row blank blank space end table table row blank blank cell fraction numerator 3 straight pi over denominator 4 end fraction end cell end table$ .