Question

How do you convert the rectangular equation $x = 4$ into polar form?

Answer 1

Hint: The equation $x = 4$ represents the line parallel to the $x$-axis whose $y$ values are $0$ in the rectangular coordinate.
The polar coordinate system is given by $(r,\theta )$ .
To convert a rectangular equation in polar form, the conversion equations of \[x = r\cos \theta \;\] and \[y = r\sin \theta \;\] are used.
Substitute $x = 4$ into the equation \[x = r\cos \theta \;\] to get the required equation.

Complete step-by-step answer:
Convert the rectangular equation $x = 4$ into polar form. To convert a rectangular equation in polar form, the conversion equations of \[x = r\cos \theta \;\] and \[y = r\sin \theta \;\] are used.
Substitute $x = 4$into the equation \[x = r\cos \theta \;\].
\[4 = r\cos \theta \;\]
\[ \Rightarrow r = \dfrac{4}{{\cos \theta }}\]

Final Answer: The polar form of the rectangular equation $x = 4$is \[ \Rightarrow r = \dfrac{4}{{\cos \theta }}\].

Note:
Iif \[(r,\theta )\;\] is a polar coordinate is given, substitute $r$ and $\theta $ into the equation for \[x = r\cos \theta \;\] and \[y = r\sin \theta \;\] to get \[(x,y).\]
The same holds true for if you are given an \[(x,y)\] a rectangular coordinate instead.
To convert from polar to rectangular:
\[x = r\cos \theta \;\]
\[y = r\sin \theta \;\]
To convert from rectangular to polar:
\[{r^2} = {x^2} + {y^2}\]
\[\tan \theta = \dfrac{y}{x}\]