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13) An air traffic controller's radar display uses polar coordinates. A passing plane is detected at ° counter-clockwise from north at a distance of miles from the radar. Thirty seconds later the plane is detected at ° and miles. Estimate the plane's speed in miles per hour. Create your own worksheets like this one with Infinite Precalculus.
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MA 114 Worksheet 25: Polar Coordinates I 1. Convert from rectangular to polar coordinates: (a) (1, √ 3) (b) (−1,0) (c) (2,−2) 2. Convert from polar to rectangular coordinates: (a) 2, π 6 (b) −1, π 2 (c) 1,− π 4 3. List all the possible polar coordinates for the point whose polar coordinates are (−2,π/2). 4. Sketch the graph of ...
A curve C1 has polar equation r = 2sin θ, 0 2≤ <θ π . a) Find a Cartesian equation for C1, and describe it geometrically. A different curve C2 has Cartesian equation 4 2 1 2 x y x = −, x ≠ ± 1. b) Find a polar equation for C2, in the form r f= (θ). x y2 + − =( )1 12, r = tan θ
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coordinates. polar coordinate system, gives the co-ordinates of a point with reference to a point O and a half line or ray starting at the point O. We will look at polar coordinates for points in the xy-plane, using the origin (0; 0) and the positive x-axis for reference.
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2.Convert (2; 2) to polar coordinates. Give two possible answers. Solution: r= p 22 +22 = 2 p 2, and = arctan(2 2) = ˇ 4. So we have (r; ) = (2 p 2; ˇ 4). Another possibility is (2 p 2;7ˇ 4), or ( 2 p 2;3ˇ 4). 3.Give rectangular coordinates for these points: (a)(r; ) = (3;5ˇ 4) Solution: (3 p 2 2; 3 p 2 2) (b)(r; ) = ( 4;11ˇ 6) Solution ...
Worksheet by Kuta Software LLC-3-Convert each pair of rectangular coordinates to polar coordinates where r > 0 and 0 £ q < 2p. 13) (3, 0) (3, 0) 14) (2, 23) (4, p 3) 15) (-2 2, 2 2) (1, 3p 4) 16) (1 2, - 3 2) (1, 5p 3) Convert each equation from rectangular to polar form. 17) y = 5x tanq = 5 18) x2 + (y - 1) 2 = 1 r = 2sinq 19) y = x2 5 r ...
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AP Calculus BC Worksheet: Polar Coordinates. 1. The area inside the polar curve r = 3 + 2cos q is. 9.425. 18.850. 28.274. 34.558. 69.115. 2. The area enclosed inside the polar curve r2 = 10 cos (2q) is. 10. 5p. 20. 10p. 25p is. 7. The graphs of the polar curves r = 2 and r = 3 + 2cos q are shown in the figure below. The curves intersect. q 2p q 4p.
