Thread: Rectangular form of an equation

1. Rectangular form of an equation

I have to put 2(cos(pi/3)+isin(pi)/3) into rectangular form. I need some help as to where to begin. Can anyone help? Thanks.

2. Originally Posted by Joanie
I have to put 2(cos(pi/3)+isin(pi)/3) into rectangular form. I need some help as to where to begin. Can anyone help? Thanks.
Greetings,

You can use Euler's Identity (AKA Euler's Formula): $re^{i\theta} \; = \; rcos(\theta) \; + \; irsin(\theta)$

This can be converted to Cartesian coordinates using: $z \; = \; x \; + \; iy$

So,
$z \; = \; re^{i\theta}$
$x \; = \; rcos(\theta)$
$y \; = \; irsin(\theta)$

Hopefully that helps.

3. Originally Posted by Joanie
I have to put 2(cos(pi/3)+isin(pi)/3) into rectangular form.
What is the value of cos(pi/3)? What is the value of sin(pi/3)? Plug these values in.

Then multiply through by the "2". This will give you the "x + iy" form (which I'm guessing is what you need).

4. Your response to my question

Thank you for helping. When I followed your advice, I came up with the answer 1 + square root of 3 i

Joanie