To find: The area of the common region enclosed by the circles
Answer to Problem 51E
The area of the region enclosed by the given circles is
Explanation of Solution
Given information: Equations of two circles are
Formula used: The double-angle formula of cosine function is given by
The quotient identity of tangent function is
Calculation:
Find the intersection point of
Draw the region enclosed by the given circles as shown below.
Figure (1)
Area of the shaded region as shown in the figure is given by the integral.
So, the area of the common region enclosed by the circles
To find the required area, solve the integral.
Further simplify.
Therefore, the required area enclosed by the circles is
Chapter 10 Solutions
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