Please Discuss here about this assignment.Thanks
Our main purpose here discussion not just Solution
We are here with you hands in hands to facilitate your learning and do not appreciate the idea of copying or replicating solutions.
1) Symmetry about the Initial Line
If the equation of a curve remains unchanged when (r,θ)
is replaced by either (r,-θ) in its equation ,then the curve
is symmetric about initial line.
(ii) Symmetry about the y-axis
If when (r, θ) is replaced by either (r,π θ − ) in
The equation of a curve and an equivalent equation
is obtained ,then the curve is symmetric about the
line perpendicular to the initial i.e, the y-axis
(ii) Symmetry about the Pole
If the equation of a curve remains unchanged
when either (-r, θ) or is substituted for (r, θ)
in its equation ,then the curve is symmetric
about the pole. In such a case ,the center of
the curve.
Answer # 1:
Equation of the curve in polar co-ordinates is r2=-4sin2θ
(i) Symmetry about the Initial Line.
r2=-4sin2θ
Remember that sine is an odd function
Put (r,-θ) in equation
r2=-4sin2 (-θ)
r2=-4sin (-2θ)
r2=4sin2θ
This equation is not symmetry about initial line
(ii) Symmetry about the Pole
r2=-4sin2θ
Put (-r, θ) in equation
(-r) 2 =-4sin2θ
r2=-4sin2θ
This equation is symmetry about pole
Q:1:- Equation of the curve in polar co-ordinates is =-4sin2 discuss the symmetry of graph of this curve about.
Initial line
Pole
Equation of the curve in polar co-ordinates is
=-4sin2θ
Symmetry about the Initial Line.
=-4sin2θ
sin is odd function.
Put (r, -θ) in equation
=-4sin2 (-θ)
=-4sin (-2θ)
=4sin2θ
this equation is not symmetry about initial line
Symmetry about the Pole
=-4sin2θ
Put (-r, θ) in equation
=-4sin2θ
=-4sin2θ
This equation is symmetry about pole
© 2021 Created by + M.Tariq Malik. Powered by
Promote Us | Report an Issue | Privacy Policy | Terms of Service
We non-commercial site working hard since 2009 to facilitate learning Read More. We can't keep up without your support. Donate.
We are user-generated contents & non-commercial site. All product, videos, pictures & others contents on site don't seem to be beneath our Copyrights & belong to their respected owners & freely available on public domains. All Contents on site are for personal & non-commercial use.We believe in Our Policy & do according to them. If Any content is offensive in your Copyrights then please email at m.tariqmalik@gmail.com with copyright detail & We will happy to remove it immediately.
Management: Admins ::: Moderators
Awards Badges List | Moderators Group
All Members | Featured Members | Top Reputation Members | Angels Members | Intellectual Members | Criteria for Selection
Become a Team Member | Safety Guidelines for New | Site FAQ & Rules | Safety Matters | Online Safety | Rules For Blog Post