To match each of the conversion formulas to the correct conversion type and complete the sentence regarding the polar coordinate system, we proceed as follows:
1. For the formula [tex]\(\theta = \tan^{-1}\left(\frac{y}{x}\right)\)[/tex]:
- This formula is used to find the angle [tex]\(\theta\)[/tex] in polar coordinates.
- The correct conversion type for this formula is "ث".
2. For the formula [tex]\(x = r \cos \theta\)[/tex]:
- This formula is used to convert from polar coordinates to Cartesian coordinate [tex]\(x\)[/tex].
- The correct conversion type for this formula is "[tex]$\hat{\sim}$[/tex]".
3. For the formula [tex]\(r = \sqrt{x^2 + y^2}\)[/tex]:
- This formula is used to find the radius [tex]\(r\)[/tex] in polar coordinates.
- The correct conversion type for this formula is "今े".
4. For the formula [tex]\(y = r \sin \theta\)[/tex]:
- This formula is used to convert from polar coordinates to Cartesian coordinate [tex]\(y\)[/tex].
- The correct conversion type for this formula is "[tex]$\hat{\sim}$[/tex]".
5. In the polar coordinate system, the point [tex]\((0,0)\)[/tex] is called the origin.
Based on the above steps, the completed table and sentence will be:
\begin{tabular}{|c|c|c|}
\hline
[tex]\(\theta = \tan^{-1}\left(\frac{y}{x}\right)\)[/tex] & ث \\
\hline
[tex]\(x = r \cos \theta\)[/tex] & [tex]$\hat{\sim}$[/tex] \\
\hline
[tex]\(r = \sqrt{x^2 + y^2}\)[/tex] & 今े \\
\hline
[tex]\(y = r \sin \theta\)[/tex] & [tex]$\hat{\sim}$[/tex] \\
\hline
\end{tabular}
In the polar coordinate system, the point [tex]\((0,0)\)[/tex] is called the origin.
