To convert the rectangular equation [tex]\( x = 3 \)[/tex] to its polar form, we need to use the relationships between rectangular coordinates [tex]\((x, y)\)[/tex] and polar coordinates [tex]\((r, \theta)\)[/tex].
In polar coordinates:
[tex]\[ x = r \cos \theta \][/tex]
[tex]\[ y = r \sin \theta \][/tex]
Given the equation [tex]\( x = 3 \)[/tex], we can substitute the polar coordinate expression for [tex]\( x \)[/tex] into the equation:
[tex]\[ r \cos \theta = 3 \][/tex]
Now, solving for [tex]\( r \)[/tex]:
[tex]\[ r = \frac{3}{\cos \theta} \][/tex]
This expression tells us that the radius [tex]\( r \)[/tex] in polar coordinates is [tex]\( \frac{3}{\cos \theta} \)[/tex] when [tex]\( x = 3 \)[/tex].
Thus, the correct polar form of the equation [tex]\( x = 3 \)[/tex] is:
[tex]\[ r = \frac{3}{\cos \theta} \][/tex]
Therefore, the correct answer is:
[tex]\[ r = \frac{3}{\cos \theta} \][/tex]
