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Polar+Graphs

# Polar+Graphs - 732 CI-IAP’I‘ER9 Poiar...

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Unformatted text preview: 732 CI-IAP’I‘ER9 Poiar Coordinates;Vectars Table 1 Description Rectangular equation Polar equation Trek-1| graph Line passing through the pole making an angle a with the polar axis y = (tan a)x ﬂ 7" a n Vertical line x = a r cos 6 = a 1'4 Harizontal line r=b rsin9=b 7! Description Rectangular equation Polar equation Typical graph Center at the pole, radius a x1+y2=a1. a>0 rwa, a>0 H Passing through the pole. qr tangentto the line 8 z 3-, center on the polar axis. radius a - x2 + y‘ 2 ﬂax. a > 0 r=i2acos€, a>0 1% Passing through the pole, tangent to the polar axis, center on the line 9 = 1. radius a 2 x2+y2=i2ay. a>0 r=:l:2.asin9, a>0 1“ Limacon witl-uom inner 100;: Name Cardioid Limagzon with inner loop Polarequations rwaiacoss, a>0 r=aibcosa, 0<b<a r=aibcosﬂ, 0<a<b r‘zazhaslne, a>0 r=aibsin6. 0<b<a r=aibsin6. 0<a<b a. a.‘ 0‘)? x x T “31-1) _ 6-... NH: Name Lemniscate Rose with three petals Rose With four petals :- = a sin(39), a > 0 r = a sin(29). a > 0 r = acos(38}, .a > 0 r 3 a c0596), 0 > O y; H r? = a1 mm), a > o r2 = 92 sin(26), a > 0 Polar equations Typicai graph ...
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