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gr 13. r 2 sin 0 = of ec

gr 13. r 2 sin 0 = of ec

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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82 32 r = a cose 14. r = 3 cos 0 ............In General a>0 a Equations Relating Polar and Cartesian Coordinates x = r cos 0, y = r sin 0, p² = x² + y², + T 16. r = -cos 0 82 + + a BIN tan 0 = Sketch the graph of each polar equation. Also, convert each into a rectangular coordinate equation. 13. r 2 sin 0 15. r = -sin 0 17. r cos=-4 r = asin 0 32 a>0 +
Transcribed Image Text:82 32 r = a cose 14. r = 3 cos 0 ............In General a>0 a Equations Relating Polar and Cartesian Coordinates x = r cos 0, y = r sin 0, p² = x² + y², + T 16. r = -cos 0 82 + + a BIN tan 0 = Sketch the graph of each polar equation. Also, convert each into a rectangular coordinate equation. 13. r 2 sin 0 15. r = -sin 0 17. r cos=-4 r = asin 0 32 a>0 +
4) Find the Cartesian coordinates of the following points (giver polar coordinates). a. (√2, π/4) c. (0, π/2) 5) Graph the polar equations. a) r = 2 b. (1,0) d. (-√2, π/4) b) = π/3, -1≤r≤ 3 6) Change the polar equation into rectangular form and describe the graph. a) r cos 0 = 2 b) rcos + r sin 0 = 1 7) Change the rectangular form into a polar equation a) x² + y² = 4 2² ô + 4 e. (-3,5π/6) g. (-1,7m) = 1 f. (5,tan-¹(4/3)) h. (2√3, 2π/3) c) r² = 1
Transcribed Image Text:4) Find the Cartesian coordinates of the following points (giver polar coordinates). a. (√2, π/4) c. (0, π/2) 5) Graph the polar equations. a) r = 2 b. (1,0) d. (-√2, π/4) b) = π/3, -1≤r≤ 3 6) Change the polar equation into rectangular form and describe the graph. a) r cos 0 = 2 b) rcos + r sin 0 = 1 7) Change the rectangular form into a polar equation a) x² + y² = 4 2² ô + 4 e. (-3,5π/6) g. (-1,7m) = 1 f. (5,tan-¹(4/3)) h. (2√3, 2π/3) c) r² = 1
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