The second graph shown the polar curve at r = 7.
Given ,
Equation of polar curve = r = 2 + 5sin(θ)
We have to find ,
Which of following graph show polar curve ,
At r = 2 + 5sin(θ)
The area between two curves in the polar coordinate system, first find the points of intersection, then subtract the corresponding areas.
First graph ; r = 2 + 5sin(θ)
Where ,
[tex]\theta = 0[/tex]
r = 2 + 5sin0
r = 2 + 5 (0)
r = 2
Second graph : r = 2 + 5sin(θ)
Where
[tex]\theta = \frac{\pi }{2}[/tex]
Then,
r = 2 + sin[tex]\frac{\pi }{2}[/tex]
r = 2 +5 ( 1 )
r = 2+5
r = 7
Third graph ; r = 2 + 5sin(θ)
where
[tex]\theta = \pi[/tex]
Then,
r = 2 + 5sin[tex]\pi[/tex]
r = 2 + 5(0)
r = 2
Fourth graph ; r = 2 + 5sin(θ)
Where
r = 2 + 5sin[tex]\frac{3\pi }{2}[/tex]
r = 2 + 5 (-1)
r = -3
Fifth graph ; r = 2 + 5sin(θ)
Where
[tex]\theta = 2\pi[/tex]
r = 2 + 5sin(2π)
r = 2+ 5 (0)
r = 2
Comparing all the value of the graph ,the second graph shown the polar curve at r = 7.
Hence, The second graph shown the polar curve at r = 7.
For more information about Polar curves click the link given below.
https://brainly.com/question/1094340
