Question

How do you write the rectangular equation $ y = 5 $ in polar form?

Answer 1

Hint: Polar coordinate system is well defined as the two-dimensional coordinate system in which each point on the plane and which is determined by the distance from the reference point and an angle from a reference direction. To get the polar form of the rectangular equation we will use the formula $ x = r\cos \theta $ and $ y = r\sin \theta $ then find the correlation between the two and will simplify accordingly for the required resultant solution.

Complete step-by-step answer:
Given expression: $ y = 5 $
We have following two equations in the polar form –
 $
  x = r\cos \theta \\
  y = r\sin \theta \;
  $
Now, place the given term value in the above equation –
 $ 5 = r\sin \theta $
Make the required term “r” the subject, when the term is multiplicative at one side if moved to the opposite side then it goes to the denominator.
 $ r = \dfrac{5}{{\sin \theta }} $
Using the sine inverse function which is equal to the cosine angle. Simplify the above expression -
 $ r = 5\cos ec\theta $
This is the required solution of the given rectangular equation in the polar form.
So, the correct answer is $ r = 5\cos ec\theta $ ”.

Note: Always Know the difference between the polar and cartesian coordinates. Cartesian coordinates are defined as exactly one set of coordinates for any given point and polar coordinates are expressed as the infinite number of coordinates for the given point.