Question

How do you find the rectangular coordinate for [3, pi/2]?

Answer 1

Hint: To do this question first you should know the conversion of polar coordinates to rectangular coordinates. The formulas for that are $x = r \cos\theta$ and $y = r\sin\theta$. From the question you can take the value of r and $\theta$. r = 3 and $\theta = \dfrac{\pi}{2}$. Now you can substitute these value sin the equations, to get the rectangular coordinates x and y.

Complete step-by-step answer:
Here is the step wise solution.
The first to do in order to solve this question is to write the formulas for the conversion of polar coordinates to rectangular coordinates. The formulas are $x = r \cos\theta$ and $y = r\sin\theta$.
Now we need to know the value of r and $\theta$. In the question, these values are given as r = 3 and $\theta = \dfrac{\pi}{2}$..
The next step is just to substitute these values in the above formulas to get the final answer for the rectangular coordinates that is x and y. Hence, we get:
First we find the x coordinate
$\Rightarrow x = r \cos\theta$
$\Rightarrow x = 3 \cos\left(\dfrac{\pi}{2}\right) $
$\Rightarrow x = 0$
Next we find the y coordinate
$\Rightarrow y = r \sin\theta$
$\Rightarrow y = 3 \sin\left(\dfrac{\pi}{2}\right) $
$\Rightarrow y = 3$
Therefore, we get the final answer of the question, how do you find the rectangular coordinate for [3, pi/2], as x = 0, y = 3, that is $\left(0,3\right)$.

Note: To do this question, you need to know the formulas for the conversion of polar to rectangular coordinates. You can recheck your answers, by converting the rectangular coordinates to polar coordinates and check if it matches with the question.