Chapter 9.5, Problem 51E

To determine

To calculate: To convert the rectangular equation to polar form

Answer to Problem 51E

The polar equation is $r=a\csc \theta$

Explanation of Solution

Given information: Rectangular equation is $y=a$

Formula Used:

Polar coordinate of a point $\left(r,\theta \right)$ in rectangular form is given as

  $\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$

Calculation:

Rectangular equation is given as

  $y=a$

Substituting $x=r\cos \theta ;y=r\sin \theta$ in above equation:

  $\begin{array}{l}r\sin \theta =a\\ r=\frac{a}{\sin \theta }\\ r=a\csc \theta \end{array}$

Thus, polar equation is $r=a\csc \theta$

Conclusion:

Hence, polar equation is $r=a\csc \theta$