\displaystyle{\left(-{1},\frac{{{3}\pi}}{{2}}\right)} lies on the polar graph

Cheyanne Leigh 2021-02-26 Answered

The reason ehy the point (1,3π2) lies on the polar graph r=1+cosθ even though it does not satisfy the equation.

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Expert Answer

crocolylec
Answered 2021-02-27 Author has 100 answers

The given equation of the polar curve is r=1+cosθ.
By substituing the point (1,3π2)r=1+cosθ
r=1+cosθ
1=1+cos(3π2)
1=1+0
11
Therefore, the point (1,3π2) does not satisfy the equation of the polar curve r=1+cosθ.
Use online graphing calculator and draw the graph of r=1+cosθ as shown below in Figure 1 and identify the point (1,3π2).
image
From Figure 1 it can be noted that the point (1,3π2) lies on the graph.
Consider the point (1,3π2) and change its radial coordinate to 1 and subtract π from the directional coordinate to obtain the alternate representation of the point (1,3π2).
Therefore, the point (1,3π2) can also be represented by (1,3π2π)=(1,π2).
By substituing the point (1,π2)r=1+cosθ,
r=1+cosθ
1=1+cos(π2)
1=1+0
1=1
Thus, the point (1,π2) satisfies the polar equation r=1+cosθ.
And from Figure 1 it can be seen that the points (1,π2)and(1,3π2) are the same points.
Therefore, due to this multiple identity, the point (1,3π2) lies on the graph even if does not satisfy the polar equation r=1+cosθ

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