00:04
We're given points in rectangular coordinates and we have to change to spherical coordinates.
00:11
In part a, we're given the point x, y, z, with rectangular coordinates 0, negative 2, 0.
00:22
Defined the spherical coordinates, we'll use the conversion equations.
00:29
So we have that row is equal to the square root of x squared plus y squared plus z squared.
00:35
This is the square root of negative 2 squared, which is positive 2.
00:46
Now to find phi, well, we know that phi satisfies z equals row times the cosine of phi.
00:55
Therefore, the cosine of phi is equal to z over row, which is 0 over 2, which is 0.
01:06
And therefore since phi lies between 0 and pi, it follows that phi is equal to pi over 2.
01:21
Now define theta, well, we know that x is equal to row times the sine of phi times the cosine of theta.
01:35
Therefore, the cosine of theta is equal to x over row times the sign of phi.
01:41
Plugging in values this is 0 over 2 times the sign of pi over 2 this is simply 0 over 2 0 over 2 times 1 or 0 so theta is therefore equal to pi over 2 or 3 pi over 2 now if theta were equal to pi over 2 then why would be positive but y of course is negative.
02:25
This implies that theta must be equal to net 3 pi over 2.
02:32
Therefore in spherical coordinates we have the point row theta phi, the coordinates 2, 3 pi over 2, pi over 2...