Theory of Intelligence
11TH•Mathematics•Complex Numbers•Question 1

(vii) $(\dfrac{9}{2},\dfrac{19\pi}{12})$

Plot the following points:

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(vii) (92,19π12)(\dfrac{9}{2},\dfrac{19\pi}{12})

Here r=92>0r=\dfrac{9}{2}>0.

19π12=2π−5π12\frac{19\pi}{12}=2\pi-\frac{5\pi}{12}

So it lies in Quadrant IV.

Use:

cos⁡19π12=cos⁡5π12=6−24,sin⁡19π12=−sin⁡5π12=−6+24\cos\frac{19\pi}{12}=\cos\frac{5\pi}{12}=\frac{\sqrt{6}-\sqrt{2}}{4},\quad \sin\frac{19\pi}{12}=-\sin\frac{5\pi}{12}=-\frac{\sqrt{6}+\sqrt{2}}{4} x=92cos⁡19π12=9(6−2)8y=92sin⁡19π12=−9(6+2)8\begin{aligned} x&=\frac{9}{2}\cos\frac{19\pi}{12}=\frac{9(\sqrt{6}-\sqrt{2})}{8}\\ y&=\frac{9}{2}\sin\frac{19\pi}{12}=-\frac{9(\sqrt{6}+\sqrt{2})}{8} \end{aligned}

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