Answer:
The point is [tex](-\frac{9}{2},\frac{9\sqrt{3}}{2},3)[/tex] in rectangular coordinates.
Step-by-step explanation:
To convert from cylindrical to rectangular coordinates we use the relations
[tex]x=r \cdot cos(\theta)\\y=r\cdot sin(\theta)\\z=z[/tex]
To convert the point [tex](9,\frac{2}{3}\pi ,3)[/tex] from cylindrical to rectangular coordinates we use the above relations
Since [tex]r=9[/tex], [tex]\theta=\frac{2}{3} \pi[/tex], and [tex]z=3[/tex],
[tex]x=r \cdot cos(\theta)=9\cdot cos(\frac{2}{3}\pi )=-\frac{9}{2}[/tex]
[tex]y=r\cdot sin(\theta)=9\cdot sin(\frac{2}{3} \pi )=\frac{9\sqrt{3}}{2}[/tex]
[tex]z=z=3[/tex]
Thus, the point is [tex](-\frac{9}{2},\frac{9\sqrt{3}}{2},3)[/tex] in rectangular coordinates.
