Replace the Cartesian equations with equivalent polar equations. x = 7

Question

Mohammad Cantrell · Accepted Answer

Since   x  =  r  cos  ⁡  θ , so an equivalent polar equation is   r  cos  ⁡  θ  =  7. Another is   r  =  7  sec  ⁡  θ if we multiply both sides by   sec  ⁡  θ to isolate r.Polar coordinates and Cartesian coordinates conversion:  r  =            x              2              +          y              2              θ  =      tan          −      1        ⁡  (      y    x    )  x  =  r  cos  ⁡  θ  y  =  r  sin  ⁡  θResult:  r  cos  ⁡  (  θ  )  =  7

Deja Bradshaw · Accepted Answer

The goal of the exercise is to convert the given equation of cartesian coordinates
x=7
into polar coordinates.
Let's recall that the polar coordinates r and

θ

are given as

r^{2} = x^{2} + y^{2}, \tan θ = \frac{y}{x}

...(1)
in terms of cartesian coordinates and the cartesian coordinates x and y are given as

x = r \cos θ, y = r \sin θ

...(2)
To convert the given equation into cartesian coordinates let's substitute

x = r \cos θ

in the given equation using the formula given in Eq. (2)

r \cos θ = 7

;
Result:

r \cos θ = 7

Replace the Cartesian equations with equivalent polar equations. x = 7

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