BC^CALCULUS
Alabama School of Mathematics and Science
1255 Dauphin Street, Mobile, AL 36604

Learning Modules/BC^Calculus/C.Akkoc/1996

MODULE No.1

CHARACTERISTICS of GRAPHS in POLAR COORDINATES


Construct the graphs for the following functions on PLOT in:

CARTESIAN Coordinates:

(a) f1(x) = sin(2x) * cos(3x); X[0,6.3], Y[-1.1,1.1]

(b) f2(x) = sin(2x) + cos(3x); X[0,8.0], Y[-2.2,2.2]

(c) f1 + f2; X[0,8], Y[-1.5,3]


POLAR Coordinates:

(a) r1(t) = sin(2t) * cos(3t); X[-0.7,0.6], Y[-0.8,.15]

(b) r2(t) = sin(2t) + cos(3t); X[-1.5,1.3], Y[-1.7,1.7]

(c) r1 + r2; X[-2.2,1.6], Y[-2.7,1]



Determine the PERIOD of each function through computations, if you can, or by examining the graph in the two coordinate systems:

(a) f1 (Period=___________________); r1 (Period=___________________)

(b) f2 (Period=___________________); r2 (Period=___________________)

(c) f1+f2 (Period=___________________); r1+r2 (Period=___________________)

Do the periods in the two coordinate systems match in: (a:Yes__,No__), (b:Yes__,No__), (c:Yes__,No__) ?. How do you explain those cases where the periods in the two coordinate systems do not match ?

Explanation:
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Make a hard copy of each graph on the dot matrix printer. Find all zero-crossings: x-coordinates on the Cartesian Plane and pole-crossings: theta-coordinates on the Polar Plane both analytically, if you can, and/or graphically by "zeroing in" on the zero crossings with the cursor to get an estimate.



(a) f1;r1: X (zero crossings) = ___________________________ t (pole crossings) = __________________

(b) f2;r2: X (zero crossings) = ___________________________ t (pole crossings) = __________________

(c) f1+f2;r1+r2: X (zero crossings) = _____________________ t (pole crossings) = __________________


Do the zero and pole-crossings match on the two type of graphs? Mark by hand on polar graphs, on the hard copy, points corresponding to the zero-crossings in the Cartesian graph.

What conclusions can you draw from this exercise with reference to constructing graphs in RECTANGULAR vs POLAR coordinates ?

Conclusions:


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Put your name on the hard copies(6)/this cover sheet/the calculations sheet and turn it in.

Name:_____________________ Date:_________________

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