Question

how do I convert the rectangular equation: x=15 to a polar equation that expresses r in terms on theta?I got r=15 sectheta but wanted to double check

Answer 1

In polar coordinates, the x variable is given as

`x=r\cos \theta`

So, we have the equation

`r\cos \theta=15`

By dividing both sides by cosine of thetat, we get

`r=(15)/(\cos \theta)`

since

`\sec \theta=(1)/(\cos \theta)`

The above result is equivalent to:

`r=15\sec \theta`