In problems 1-3 do the following: (a) Sketch a rectangular plot of the given equation in the Or- plane over the indicated 0 interval. (b) Sketch a polar plot of the equation in the xy - plane, where x = r cos 0, y = r sin 0. (c) Find the slope and inclination of the tangent line to the polar curve at the point P = (x, y) = (r · cos ,1 ‚r.sin) by using the fact that: Slope at P = dy dx P = dy/de dx/de 0 = 퓨 (Refer to the notes at Topic 12: Slopes to Curves in Polar Coordinates for details on this topic. Polar graph paper templates may be downloaded at Polar Graph Paper Templates (pdf). 1. r = 2 cos 0 ; 0 ≤ 0 ≤ π 2. r = 2 + 2 sin 0; 0 ≤ 0 ≤ 2π 3. r 2 sin(30) ; 0 ≤ 0 ≤ π
In problems 1-3 do the following: (a) Sketch a rectangular plot of the given equation in the Or- plane over the indicated 0 interval. (b) Sketch a polar plot of the equation in the xy - plane, where x = r cos 0, y = r sin 0. (c) Find the slope and inclination of the tangent line to the polar curve at the point P = (x, y) = (r · cos ,1 ‚r.sin) by using the fact that: Slope at P = dy dx P = dy/de dx/de 0 = 퓨 (Refer to the notes at Topic 12: Slopes to Curves in Polar Coordinates for details on this topic. Polar graph paper templates may be downloaded at Polar Graph Paper Templates (pdf). 1. r = 2 cos 0 ; 0 ≤ 0 ≤ π 2. r = 2 + 2 sin 0; 0 ≤ 0 ≤ 2π 3. r 2 sin(30) ; 0 ≤ 0 ≤ π
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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Transcribed Image Text:In problems 1-3 do the following:
(a) Sketch a rectangular plot of the given equation in the Or- plane over the indicated 0 interval.
(b) Sketch a polar plot of the equation in the xy - plane, where x = r cos 0, y = r sin 0.
(c) Find the slope and inclination of the tangent line to the polar curve at the point
P = (x, y) = (r · cos ,1
‚r.sin) by using the fact that:
Slope at P =
dy
dx P
=
dy/de
dx/de
0 =
퓨
(Refer to the notes at Topic 12: Slopes to Curves in Polar Coordinates for details on this topic. Polar graph
paper templates may be downloaded at Polar Graph Paper Templates (pdf).
1. r = 2 cos 0 ; 0 ≤ 0 ≤ π
2. r = 2 + 2 sin 0; 0 ≤ 0 ≤ 2π
3. r 2 sin(30) ; 0 ≤ 0 ≤ π
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