Question

3. Write the equation+ cylindrical coordinates and (b) spherical coordinates. 1 in (a) 4. Sketch the solid described by the given inequalities. For help with visualizing Spherical Restrictions: https://ggbm.at/hhh8wgpc 1< p3 and 00 2 2 tY

Need help with both of these... Thanks

Answer 1

(3)

(a)

in cylindrical coordinates,

x r cos, y rsin0,z z

we have

x²=r²cos²$\large \theta$

y²=r²sin²$\large \theta$ and

z²=z²

our equation becomes

(r²cos²$\large \theta$ )/4 + (r²sin²$\large \theta$ )/9 + z²/(1/4)=1

where r²=x²+y²

and  $\large \theta$ = tan^-1(y/x)

(b)

in spherical coordinates,
x p sin cos, y p sind sin,z= p cos

=> x²=$\large \rho$²sin²$\large \phi$cos²$\large \theta$

y²=$\large \rho$²sin²$\large \phi$sin²$\large \theta$ and

z²=$\large \rho$²cos²$\large \phi$

so our equation becomes

($\large \rho$²sin²$\large \phi$cos²$\large \theta$)/4 + ($\large \rho$²sin²$\large \phi$sin²$\large \theta$)/9 + ($\large \rho$²cos²$\large \phi$)/(1/4) =1

where

$\large \rho$²= x²+y²+z²

$\large \theta$=tan^-1(y/x)

$\large \phi$=tan^-1 ((√(x²+y²))/z)