Question

A point is given in rectangular coordinates. Convert the point to polar coordinates (r > 0, 0 ≤ < 2).(9, 9)

Answer 1

In order to convert a point from rectangular coordinates (x, y) to polar coordinates (r, θ), we can use the following:

`\begin{gathered} r=\sqrt[]{x^(2)+y^(2)} \\ \\ \tan \theta=(y)/(x) \end{gathered}`

In this problem, we need to convert to polar coordinates the point (9, 9). So, we have:

x = 9

y = 9

Then, using those values in the above formulas, we obtain:

`\begin{gathered} r=\sqrt[]{9^(2)+9^(2)}=\sqrt[]{2\cdot9^(2)}=9\sqrt[]{2} \\ \\ \tan \theta=(9)/(9)=1\text{ }\Rightarrow\text{ }\theta=(\pi)/(4)\text{ because }\tan (\pi)/(4)=1 \end{gathered}`

So, in polar coordinates, this point is written as

`\mleft(9\sqrt[]{2},(\pi)/(4)\mright)`