Find the points of intersection of the graphs of the equations r = 1 + sin θ,       r = 3 sin θ

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find the points of intersection of the graphs of the equations r = 1 + sin θ,       r = 3 sin θ

Expert Solution
Step 1 Given equations:

r = 1 + sin θ,       r = 3 sin θ

To find: The points of intersection of the graphs of the equations.

Step 2 Calculations:

Equate both equations, 

1+sinθ=3 sinθ3 sinθ- sinθ=12  sinθ=1 sinθ=12         ...(i)

Since the sine function is positive in the first and the second quadrant.

Thus, the solution will be θ=π6+2πn,θ=5π6+2πn, where n is any integer.

 

 

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