Convert to Rectangular Form...6

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Mar 19, 2022.

  1. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Screenshot_20220311-155740_Samsung Notes.jpg

    Question 12

    r = 4 sin 2θ

    r = 4 (2 sin θ cos θ)

    r = 8 sin θ cos θ

    r • r = 8 r sin θ cos θ

    r^2 = 8y cos θ

    x^2 + y^2 = 8y cos θ

    Stuck here. How do I remove cos θ?
     
    nycmathguy, Mar 19, 2022
    #1
  2. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    Apply the formula
    sin(2α)=2sin(α)cos(α) with α=θ: r=8sin(θ)cos(θ).

    From x=rcos(θ) and y=rsin(θ), we have that cos(θ)= x/r, sin(θ)= y/r, tan(θ)= y/x, and cot(θ)= x/y.

    the input now takes the form
    r=8xy/r^2
    r^3=8xy
    r^3-8xy=0

    In rectangular coordinates, r= x^2+y^2

    (x^2+y^2)^3-8xy=0
     
    MathLover1, Mar 19, 2022
    #2
    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    I thought you said r = sqrt{x^2 + y^2}.
    In this reply, you said:

    "In rectangular coordinates, r= x^2+y^2."

    So, which is it?
     
    nycmathguy, Mar 19, 2022
    #3
  4. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    r = sqrt(x^2 + y^2)

    here r= x^2+y^2 made typo, should be , r^2= x^2+y^2 and when you solve it for r you get r = sqrt(x^2 + y^2)
     
    MathLover1, Mar 19, 2022
    #4
    nycmathguy likes this.
  5. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Understood. Thank you.
     
    nycmathguy, Mar 19, 2022
    #5
Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.