How do you convert r=6sectheta into cartesian form?

1 Answer
Jul 13, 2016

r = 6sec(theta) -> x=6

Explanation:

To convert from polar to cartesian, we can make use the following:

x = rcos(theta)
y = rsin(theta)
r^2 = x^2+y^2

Since r = 6sec(theta), we now have x = underbrace(6sec(theta))_(r)cos(theta)

We can simplify this expression even further since

sec(theta) = 1/(cos(theta)), so our expression becomes

x = 6/cancel(cos(theta)) * cancel(cos(theta)) = 6

So our final answer is x = 6.

We can check this by graphing, for example.
enter image source here

In this graph, x=6 and r = 6sec(theta) both overlap because they are essentially the same.