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lefthandeddolan
20.08.2020 •
Mathematics
Find the points of intersection of the graphs of the equations. r = 1 + cos θ r = 1 − sin θ r ≥ 0, 0 ≤ θ < 2π
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Ответ:
This question is based on the point of intersection.Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:
Given:
Equations: r = 1 + cos θ ...(1)
r = 1 − sin θ ...(2)
Where, r ≥ 0, 0 ≤ θ < 2π
We need to determined the point of intersection of the graphs of the equations.
To obtain the points of intersection, Equate the two equations above as follows;
r = 1 + cos θ = 1 - sin θ
=> 1 + cos θ = 1 - sin θ
Solve further for θ. We get,
1 + cos θ = 1 - sinθ
cos θ = - sinθ
Now dividing both sides by - cos θ and solve it further,
To get the 2nd quadrant value of θ, add π ( = 180°) to the value of θ. i.e
Similarly, to get the fourth quadrant value of θ, add 2π ( = 360° ) to the value of θ. i.e
Therefore, the values of θ are 3π / 4 and 7π / 4.
Now substitute these values into equations (i) and (ii) as follows;
Represent the results above in polar coordinates of the form (r, θ). i.e
Therefore, at the pole where r = 0, is also one of the points of intersection.
Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:
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