If (x, y) = (-V3, 1) , then find r and 0.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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please explain mathematically

In Calc. 3 applications, polar coordinates always obey:
(a) r = Vx2 + y² > 0
(b) 0<0 <2т.
tan (0) = y/x. Examine the Quadrants.
If (x, y) = (-V3, 1) , then findr and 0.
This must be in Quadrant II.
r =
+ 12 = V3 +1 = 2
1
tan (0)
/3)
Normally, this would give us -7/6, but this in Quadrant IV.
If we add 180°, we end up in Quad. II and 0 = 57/6.
Transcribed Image Text:In Calc. 3 applications, polar coordinates always obey: (a) r = Vx2 + y² > 0 (b) 0<0 <2т. tan (0) = y/x. Examine the Quadrants. If (x, y) = (-V3, 1) , then findr and 0. This must be in Quadrant II. r = + 12 = V3 +1 = 2 1 tan (0) /3) Normally, this would give us -7/6, but this in Quadrant IV. If we add 180°, we end up in Quad. II and 0 = 57/6.
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