Polar coordinates, maximum distance.

[xduckksx]

Homework Statement

The diagram (omitted) shows the curve C with polar equation r=e^(\theta), where 0\le\theta\le(pi/2). Find the maximum distance of a point of C from the line \theta=(pi/2), giving the answer in exact form.

The Attempt at a Solution

I'm not really sure how to attack this; it says in the examiners report that one needs to write x as e^(theta).cos(theta), but I can't see why this is...

 

[HallsofIvy]

The line $\theta= \pi/2$ is just the vertical line x= 0, the y-axis and the distance from any point (x, y) to that line is just x. And, of course, $x= r cos(\theta)$. That is what you want to maximize.

 

[xduckksx]

OMG I THOUGHT THE LINE WAS theta=pi/4 ... sigh...