Chapter 9: Q. 47 (page 756)
Use Theorem 9.14 to show that the circumference of the circle defined by the polar equation is .
Short Answer
The length of the curve is.
Chapter 9: Q. 47 (page 756)
Use Theorem 9.14 to show that the circumference of the circle defined by the polar equation is .
The length of the curve is.
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Get started for freeIn Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
Measurements indicate that Earth’s orbital eccentricity is and its semimajor axis is astronomical units.
(a) Write a Cartesian equation for Earth’s orbit.
(b) Give a polar coordinate equation for Earth’s orbit, assuming that the sun is the focus of the elliptical orbit.
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
Each of the integral in exercise 38-44 represents the area of a region in a plane use polar coordinates to sketch the region and evaluate the expression
The integral is
In Exercises 24–31 find all polar coordinate representations for the point given in rectangular coordinates.
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