Find the polar coordinates of the point whose cartesian coordinates are \((-\sqrt{2}, -\sqrt{2})\).
Q.5 Find the polar coordinates of the point whose cartesian coordinates are \((-\sqrt{2}, -\sqrt{2})\).
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Answer: \(\left(2, \frac{5\pi}{4}\right)\)
\(x = -\sqrt{2},\ y = -\sqrt{2}\). \(r = \sqrt{x^2 + y^2} = \sqrt{2 + 2} = 2\).
\(\cos\theta = \frac{x}{r} = -\frac{1}{\sqrt{2}}\) and \(\sin\theta = \frac{y}{r} = -\frac{1}{\sqrt{2}}\), so \(\theta\) lies in the third quadrant: \(\theta = \pi + \frac{\pi}{4} = \frac{5\pi}{4}\).
The polar coordinates are \(\left(2, \frac{5\pi}{4}\right)\).
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· 28 Oct 2026
AI-verified · Oct 2026
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