| \(\theta\) | \(r=2 \ \cos ( 2\theta )\) | \(( r,\theta )\) |
|---|---|---|
| \(0\) | \(2(1) =2\) | \(( 2,0)\) |
| \(\dfrac{\pi }{6}\) | \(2\left( \dfrac{1}{2}\right) =1\) | \(\left( 1,\dfrac{\pi }{6}\right)\) |
| \(\dfrac{\pi }{4}\) | \(2\left( 0\right) =0\) | \(\left( 0,\dfrac{\pi }{4}\right)\) |
| \(\dfrac{\pi }{3}\) | \(2\left( -\dfrac{1}{2}\right) =-1\) | \(\left( -1,\dfrac{\pi }{3}\right)\) |
| \(\dfrac{\pi }{2}\) | \(2\left( -1\right) =-2\) | \(\left(-2,\dfrac{\pi }{2}\right)\) |
| \(\dfrac{2\pi }{3}\) | \(2\left( -\dfrac{1}{2}\right) =-1\) | \(\left( -1,\dfrac{2\pi }{3}\right)\) |
| \(\dfrac{3\pi }{4}\) | \(2\left( 0\right) =0\) | \(\left( 0,\dfrac{3\pi }{4}\right)\) |
| \(\dfrac{5\pi }{6}\) | \(2\left( \dfrac{1}{2}\right) =1\) | \(\left( 1,\dfrac{5\pi }{6}\right)\) |
| \(\pi\) | \(2(1) =2\) | \(( 2, \ \pi)\) |
| \(\dfrac{7\pi }{6}\) | \(2\left( \dfrac{1}{2}\right) =1\) | \(\left( 1,\dfrac{7\pi }{6}\right)\) |
| \(\dfrac{5\pi }{4}\) | \(2(0) =0\) | \(\left( 0,\dfrac{5\pi }{4}\right)\) |
| \(\dfrac{4\pi }{3}\) | \(2\left( -\dfrac{1}{2}\right) =-1\) | \(\left( -1,\dfrac{4\pi }{3}\right)\) |
| \(\dfrac{3\pi }{2}\) | \(2\left( -1\right) =-2\) | \(\left( -2,\dfrac{3\pi }{2}\right)\) |
| \(\dfrac{5\pi }{3}\) | \(2\left( -\dfrac{1}{2}\right) =-1\) | \(\left( -1,\dfrac{5\pi }{3}\right)\) |
| \(\dfrac{7\pi }{4}\) | \(2\left(0\right) =0\) | \(\left( 0,\dfrac{7\pi }{4}\right)\) |
| \(\dfrac{11\pi }{6}\) | \(2\left( \dfrac{1}{2}\right) =1\) | \(\left( 1,\dfrac{11\pi }{6}\right)\) |
| \( 2\pi\) | \(2(1) =2\) | \(( 2, \ 2\pi )\) |