Theory of Intelligence
11TH•Mathematics•Complex Numbers•Exercise 1.5

Theory

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Theory

  • Polar point (r,θ)(r,\theta) corresponds to rectangular coordinates:
(x,y)=(rcos⁡θ, rsin⁡θ)(x,y)=(r\cos\theta,\ r\sin\theta)
  • If r<0r<0 then:
(r,θ)=(∣r∣,θ+π)(r,\theta)=\left(|r|,\theta+\pi\right)
  • Common exact values:
cos⁡π6=32, sin⁡π6=12,cos⁡5π12=6−24, sin⁡5π12=6+24\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2},\ \sin\frac{\pi}{6}=\frac{1}{2},\quad \cos\frac{5\pi}{12}=\frac{\sqrt{6}-\sqrt{2}}{4},\ \sin\frac{5\pi}{12}=\frac{\sqrt{6}+\sqrt{2}}{4}

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