MHT CET · Maths · Complex Number
If the Cartesian co-ordinates of a point are \(\left(\frac{-5 \sqrt{3}}{2}, \frac{5}{2}\right)\), then its polar co-ordinates are
- A \(\left(5, \frac{2 \pi}{3}\right)\)
- B \(\left(5, \frac{13 \pi}{18}\right)\)
- C \(\left(5, \frac{5 \pi}{6}\right)\)
- D \(\left(5, \frac{11 \pi}{18}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(5, \frac{5 \pi}{6}\right)\)
Step-by-step Solution
Detailed explanation
\(r=\sqrt{x^2+y^2}=\sqrt{\frac{75}{4}+\frac{25}{4}}=5 \)
\( \theta=\pi-\tan ^{-1}\left|\frac{y}{x}\right|=\pi-\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)=\pi-\frac{\pi}{6}=\frac{5 \pi}{6} \)
Polar co-ordinate \(=(r, \theta)=\left(5, \frac{5 \pi}{6}\right)\)
\( \theta=\pi-\tan ^{-1}\left|\frac{y}{x}\right|=\pi-\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)=\pi-\frac{\pi}{6}=\frac{5 \pi}{6} \)
Polar co-ordinate \(=(r, \theta)=\left(5, \frac{5 \pi}{6}\right)\)
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