Math  /  Geometry

Question(c) You are given the point (3,2)(3,2) in polar coordinates. (i) Find another pair of polar coordinates for this point such that r>0r>0 and 2πθ<4π2 \pi \leq \theta<4 \pi. r=r= θ=\theta= (ii) Find another pair of polar coordinates for this point such that r<0r<0 and 0θ<2π0 \leq \theta<2 \pi. r=θ=\begin{array}{c} r= \\ \theta= \end{array}

Studdy Solution
Find another pair of polar coordinates with r<0r < 0 and 0θ<2π0 \leq \theta < 2\pi:
For r<0r < 0, we take the opposite of the original rr: r=3 r = -3
To find θ\theta, add π\pi to the original θ\theta: θ=2+π \theta = 2 + \pi
Calculate: θ2+3.14165.1416 \theta \approx 2 + 3.1416 \approx 5.1416
Thus, another polar coordinate is: r=3 r = -3 θ5.1416 \theta \approx 5.1416
The alternative polar coordinates are: (i) r=3,θ8.2832 r = 3, \theta \approx 8.2832 (ii) r=3,θ5.1416 r = -3, \theta \approx 5.1416

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