Convert the equation r cos theta = sin (2 theta) to Cartesian coordinates. Descr

Question

Convert the equation r cos theta = sin (2 theta) to Cartesian coordinates. Describe the resulting curves. Choose the correct equations below. A. x^2+ y^2 =1^2 and x = 0 B. (x - 1)^2 (y - 1)^ and x = 0 C. (x - 1)^2 + y^2 and x = 0 D. x^2 (y - 1)^2 = 1^2 and x = 0 Choose the best description of the curves described by this equation. A. a circle centered at ( - 1,0) with a radius of 1 and the y-axis B. a circle centered at (1,0) with a radius of 1 and the y-axis C. a circle centered at (0,1) with a radius of 1 and the y-axis D. a circle centered at (0, - 1) with a radius of 1 and the y-axis

Explanation / Answer

1) r cost = sin 2t

Expand sin 2t

r cost = 2 sint cost

Thus either cost =0 or r = 2 sint

Or x =0 or x2+y2 =2y

x=0 or x2+(y-1)2=1

Option D

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Option C.

(Since centre is (0,1) and x =0 is y axis.)

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