1.9 Polar, Cylindrical, and Spherical Coordinates (continued)

Spherical Coordinates

Work through this exercise and explain your reasoning step by step.

Work through this exercise and explain your reasoning step by step.

Draw each of the points from part and show how the spherical coordinates of each point is being measured. You should use your plots to make sense of the rectangular coordinate measurements that were your answer to part.

Work through this exercise and explain your reasoning step by step.

$\phi =0$

$\phi =1$

$\phi =\frac{\pi}{2}$

$\phi =\frac{3\pi}{4}$

$\phi = \pi$

the $xy$-plane

the $xz$-plane

$z=x^2+y^2$

Work through this exercise and explain your reasoning step by step.

Draw the region described by $\rho \leq 1$ and $0 \leq \phi \leq \frac{\pi}{2}$.

Draw the region described by $x^2+y^2 \leq 9$ with $x\leq y$ and $-1 \leq z \leq 3$

Give a set of inequalities in spherical coordinates that describes the points in the seventh octant.