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Sagot :
In order to convert a point from rectangular coordinates (x, y) to polar coordinates (r, θ), we can use the following:
[tex]\begin{gathered} r=\sqrt[]{x^{2}+y^{2}} \\ \\ \tan \theta=\frac{y}{x} \end{gathered}[/tex]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:
[tex]\begin{gathered} r=\sqrt[]{9^{2}+9^{2}}=\sqrt[]{2\cdot9^{2}}=9\sqrt[]{2} \\ \\ \tan \theta=\frac{9}{9}=1\text{ }\Rightarrow\text{ }\theta=\frac{\pi}{4}\text{ because }\tan \frac{\pi}{4}=1 \end{gathered}[/tex]So, in polar coordinates, this point is written as
[tex]\mleft(9\sqrt[]{2},\frac{\pi}{4}\mright)[/tex]
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