Test for symmetry and graph each polar equation for rcosθ=-3. 5. r cos e = -3%3DTCTT2TC5TtTT36.Check for symmetrypolar axisline 0 = "2.pole 40-1010-

rcosθ=-3 Now when θ=0, rcos0=-3⇒r1=-3⇒r=-3 When θ=π6, rcosπ6=-3⇒r32=-3⇒r=-23 When θ=π3,…

Answered: r cos 0 = -3 2n 5Tt 2 3 Check for…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

Test for symmetry and graph each polar equation for rcosθ=-3.

5. r cos e = -3
%3D
TC
TT
2TC
5Tt
TT
3
6.
Check for symmetry
polar axis
line 0 = "
2.
pole

Expert Solution

Given,

$r \cos θ = - 3$

Now when $θ = 0$ ,

$r \cos (0) = - 3 \Rightarrow r (1) = - 3 \Rightarrow r = - 3$

When $θ = \frac{π}{6}$ ,

$r \cos (\frac{π}{6}) = - 3 \Rightarrow r (\frac{\sqrt{3}}{2}) = - 3 \Rightarrow r = - 2 \sqrt{3}$

When $θ = \frac{π}{3}$ ,

$r \cos (\frac{π}{3}) = - 3 \Rightarrow r (\frac{1}{2}) = - 3 \Rightarrow r = - 2 \sqrt{3}$

When $θ = \frac{π}{2}$ ,

$r \cos (\frac{π}{2}) = - 3 \Rightarrow r (0) = - 3 \Rightarrow 0 = - 3 which is not possible$

When $θ = \frac{2 π}{3}$ ,

$r \cos (\frac{2 π}{3}) = - 3 \Rightarrow r (- \frac{1}{2}) = - 3 \Rightarrow r = 6$

When $θ = \frac{5 π}{6}$ ,

$r \cos (\frac{5 π}{6}) = - 3 \Rightarrow r (- \frac{\sqrt{3}}{2}) = - 3 \Rightarrow r = 2 \sqrt{3}$

When $θ = π$ ,

$r \cos (π) = - 3 \Rightarrow r (- 1) = - 3 \Rightarrow r = 3$

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r cos 0 = -3 2n 5Tt 2 3 Check for symmetry line 0 = = pole polar axis