For a sphere parameterized using the spherical coordinates theta and phi, descri

Question

For a sphere parameterized using the spherical coordinates theta and phi, describe in words the part of the sphere given by the restrictions pi/2 lessthanorequalto theta pi 0 lessthanorequalto phi lessthanorequalto pi and 0 lessthanorequalto pi lessthanorequalto pi/6 0 lessthanorequalto phi lessthanorequalto pi/2. Then pick the figures below that match the surfaces you described. pi/2 lessthanorequalto theta lessthanorequalto pi 0 lessthanorequalto phi lessthanorequalto pi 0 lessthanorequalto theta lessthanorequalto pi/6 0 lessthanorequalto phi lessthanorequalto pi/2 (Click on any graph to see a larger version.)

Explanation / Answer

we write spherical coordinate as

x= r cos sin

y = sin sin

z= rcos

now you can see that for the given interval x <0, y>0 and z>0 as well as z<0

so this will the the part which is same as in part 3

and for second all three are positive so part 6

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