Determining 4 intersection points of two polar graphs?

  • Thread starter Tekee
  • Start date
  • #1
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Homework Statement


r = 2
r^2 = 9sin(2theta)
Find the 4 points of intersection


Homework Equations





The Attempt at a Solution


Since r = 2, 4 = 9sin(2theta)...
4/9 = sin(2theta)

Taking the inverse of 4/9 only gives me one answer on the calculator (obviously), and I do not know where to attain the 3 other points. (also, is there a way to do this without a calculator/calculus?) - IE 4/9 = 2sin(theta)cos(theta), although I do not see how this helps.
 

Answers and Replies

  • #2
6
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[tex]\sin 2\theta=\frac{4}{9}\Rightarrow 2\theta =(-1)^k\arcsin\frac{4}{9}+k\pi\Rightarrow\theta =(-1)^k\frac{\arcsin\frac{4}{9}}{2}+\frac{k\pi}{2}[/tex]
[tex]k=0\Rightarrow\theta=\frac{1}{2}\arcsin\frac{4}{9}[/tex]
[tex]k=1\Rightarrow\theta=\frac{\pi}{2}-\frac{1}{2}\arcsin\frac{4}{9}[/tex]
[tex]k=2\Rightarrow\theta=\pi+\frac{1}{2}\arcsin\frac{4}{9}[/tex]
[tex]k=3\Rightarrow\theta=\frac{3\pi}{2}-\frac{1}{2}\arcsin\frac{4}{9}[/tex]
 

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