Answer
$(x,y,z)=(\dfrac{3 \sqrt 2}{2},\dfrac{3 \sqrt 2}{2},1)$
Work Step by Step
Conversion into polar co-ordinates are: $$x= r \cos \theta ; y= r \sin \theta; z=z ~~~(1)$$
We are given that $r=3$ and $\theta=\dfrac{\pi}{4}$
Plug these values in Equation (1) to obtain: $$x=3 \cos (\dfrac{\pi}{4})=(3) \cos (\dfrac{\sqrt 2}{2})=\dfrac{3 \sqrt 2}{2} \\ y= 3 \sin (\dfrac{\pi}{4})=(3) \sin (\dfrac{\sqrt 2}{2})=\dfrac{3 \sqrt 2}{2} \\z= 1$$
This implies that $x= \dfrac{3 \sqrt 2}{2}; y=\dfrac{3 \sqrt 2}{2}; z=1$
So, our solution is: $(x,y,z)=(\dfrac{3 \sqrt 2}{2},\dfrac{3 \sqrt 2}{2},1)$
