9.2-three - 2. Graph Polar Equations Using a Graphing...

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Unformatted text preview: 2. Graph Polar Equations Using a Graphing Utility Graphing a Polar Equation Using a Graphing Utility STEP ]; Solve the equation for r in terms of 6. STEP 2: Select the viewing window in POLar mode. In addition to setting X min, X max. Xscl, and so forth, the viewing window in polar mode requires setting minimum and maximum values for 6 and an increment setting for 6 (Bstep). Finally, a square screen and radian measure should be used. Enter the expression involving 9 that you found in Step 1. (Consult your manual for the correct way to enter the expression.) Press graph. Let a be a nonzero real number. Then the graph of the equation rsinH =0 is a horizontal line :1 units above the pole if a > O and units below the pole ifa < 0. The graph of the equation rcosH = a is a vertical line (1 units to the right of the pole if a > 0 and lal units to the left of the pole ifa < O. Let a be a positive real number. Then. Equation Description (a) r = 2a sin 6 Circle: radius a: center at (0. a) in rectangular coordinates (b) r 1 -2a sin 0 Circle: radius a: center at (O. —a) in rectangular coordinates (c) r = 2a cos 6 Circle: radius a: center at ((1.0) in rectangular coordinates (d) r : —2a cos 6 Circle: radius a: center at (—61.0) in rectangular coordinates Each circle passes through the pole. 2. Test Polar Equations for Symmetgg yl e = ‘3 117 _ 1r 9’4 9—1 a B = 11' _ 5.1." B ' 4 (a) Points symmetric with (b) Points sy metric with respect to the polar axis (c) Points symmetric with respect to the pole Symmetry with Respect to the Polar Axis (x-Axis) 9 1 —'l‘|/1 ']L o “Ti/2, In a polar equation. replace 6 by *6. If an equivalent equation results. the graph is symmetric with respect to the polar axis. Symmetry with Respect to the Line 0 = % (y-Axis) A?» torn NFQLMS 6} am etc In a polar equation. replace 6 by 7.- — 6. If an equivalent equation results, the graph is symmetric with respect to the line 6 = 3. Symmetry with Respect to the Pole (Origin) In a polar equation. replace r by —r. If an equivalent equation results. the graph is symmetric with respect to the pole. 3. Graph Polar Eguations by Plotting Points Cardioids are Characterized by equations of the form = a(1 + cos 6) a(l + sin 9) a(1 -- cos 6) a(l ~— sin 6) where a > 0. The graph of a cardioid passes through the pole. Limacons without an inner loop are characterized by equations of the form where a > O. b > 0‘ and a > b. The graph of a limagon without an inner loop does not pass through the pole. Limaeons with an inner loop are characterized by equations of the form a+bc036 a+bsin€9 a—bcost? a—bsinO wherea > O, b > 0. and a < b. The graph of a limagon with an inner loop will pass through the pole twice. Rose curves are characterized by equations of the form r = acos(n6). r = asin(n€), a -+‘ 0 and have graphs that are rose shaped. If :1 ¢ 0 is even. the rose has 2n petals: ifn at $1 is odd. the rose has n petals. Lemniscates are characterized by equations of the form = a2 cos(29) where a ¢ 0. and have graphs that are propeller shaped. ...
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9.2-three - 2. Graph Polar Equations Using a Graphing...

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