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Question: The polar co-ordinates of (1, –1) is-...

The polar co-ordinates of (1, –1) is-

A

(2,π4)\left( \sqrt{2},\frac{\pi}{4} \right)

B

(−2,3π4)\left( - \sqrt{2},\frac{3\pi}{4} \right)

C

(−2,−π4)\left( - \sqrt{2},\frac{- \pi}{4} \right)

D

None

Answer

(−2,3π4)\left( - \sqrt{2},\frac{3\pi}{4} \right)

Explanation

Solution

(1, – 1)

r = x2+y2\sqrt{x^{2} + y^{2}}; r = 1+1\sqrt{1 + 1} = 2\sqrt{2}

a = tan–1 (1) = π4\frac{\pi}{4} (1, – 1) lies in IV quad.

\ q = – a q = – π4\frac{\pi}{4}

(2,–π4)\left( \sqrt{2},–\frac{\pi}{4} \right) or (–2,3π4)\left( –\sqrt{2},\frac{3\pi}{4} \right)