Chapter 9: Q. 22 (page 747)
Graph the equation in the θr-plane. Label each arc of your curve with the quadrant in which the corresponding polar graph will occur.
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In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral
The spiral
Sketch the graphs of the equations
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What is the relationship between these graphs? What is the eccentricity of each graph?
In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral
one petal of the polar rose
Measurements indicate that the orbital eccentricity of Mars is and its semimajor axis is astronomical units.
(a) Write a Cartesian equation for the orbit of Mars.
(b) Do and have the same meaning as in Exercise 53?
(c) Give a polar coordinate equation for the orbit of Mars, assuming that the sun is the focus of the elliptical orbit.
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