Chapter 11 - Vectors and the Geometry of Space - 11.7 Exercises - Page 809: 2

$(x,y,z)=(-2,0.-4)$

Relationship between cylindrical co-ordinates and rectangular co-ordinates is: $$x= r \cos \theta ; y= r \sin \theta; z=z ~~~(1)$$ We are given that $r=2$ and $\theta=-\pi$ Plug these values in Equation (1) to obtain: $$x=2 \cos (-\pi)=(2) (-1)=-2 ; y= 2 \sin (\pi)=0; z=-4$$ This implies that $x= -2; y=0; z=-4$ So, our solution is: $(x,y,z)=(-2,0.-4)$