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Polar and Parametric Equations : Eliminate the parameter to find a cartesian euqation of the curve; sketch the curve with the given polar equation. Show the equation for the sketch.

1,2,3) a) Sketch the curve by using the paramtric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.
b) Eliminate the parameter to find a cartesian euqation of the curve.

1)x = 3t-5, y=2t + 1. Part a is just making a table using t and solving for x and y, but when done with parts a and b the equation should represent the plot, but my final equation does not look like anything common to me.

2) Same thing a problem 1.
x = t^2-2, y=5-2t, (-3 <= t<= 4)

3) Same thing a problem 1.
x = SQRT t, y=1-t
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For 31 - 39, sketch the curve with the given polar equation. Show the equation solved for that represents the sketch. Tell me how you made the sketch and show every part to coming up with what you need to make the sketch without using a computer program. Have to do by hand.

31) r = sintheta, book says (1, pi/2), pic should be a circle

33) r = 2(1 - sintheta) - picture should be a cardioid

35) r = theta, theta >= 0, picture should be a dot from origin (0,0), then spirials counter clockwise and r gets bigger.

37) r = 2sintheta, book gives theta = pi/4 and picture should be a 4 petal rose, petals not on x or y axis, in between going from origin diagonally.

39) r = 2 cos 4theta, book says theta = pi/8, shows 8 petal rose.
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Solution Summary

Polar and parametric equations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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