Mathematics

Mathematics

Problem

For 0≤θ≤π/20\le \theta\le \pi/2, the polar curves r=2sin⁡θr=2\sin\theta and r=2cos⁡θr=2\cos\theta intersect at θ=π/4\theta=\pi/4. Which description correctly identifies which curve lies farther from the origin on each sub-interval? a) r=2sin⁡θr=2\sin\theta is farther for 0≤θ<π/40\le\theta<\pi/4, and r=2cos⁡θr=2\cos\theta is farther for π/4<θ≤π/2\pi/4<\theta\le\pi/2. b) r=2sin⁡θr=2\sin\theta is farther on the entire interval 0<θ<π/20<\theta<\pi/2. c) r=2cos⁡θr=2\cos\theta is farther for 0≤θ<π/40\le\theta<\pi/4, and r=2sin⁡θr=2\sin\theta is farther for π/4<θ≤π/2\pi/4<\theta\le\pi/2. d) r=2cos⁡θr=2\cos\theta is farther for 0≤θ<π/60\le\theta<\pi/6, and r=2sin⁡θr=2\sin\theta is farther for π/6<θ≤π/2\pi/6<\theta\le\pi/2.

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