00:01
In this exercise, we have a point in cartesian coordinates x, y, z, equal to 211.
00:08
And we want to find the coordinates, the circle coordinates of this point.
00:14
So remember that x is equal to r times the sign of the polar angle theta times the cosine of the azimuthal angle phi.
00:27
Y is equal to r times sine of theta times sine of five and z is equal to r times the cosine of theta so notice first of all that r is equal to the square root of x squared plus y squared plus z squared so this is equal to two squared which is four plus one plus one so this is the square root of six then notice that if we take y and divided by x, we have r, sine theta, sine phi, or here we should have phi, not a theta, i'm sorry, divided by r, sine theta, cosine, we have the tangent of phi.
01:36
So if we want to calculate the angle phi, we need to take the arc tangent of y over x.
01:50
So phi is the arc tangent of 1 over 2, which is equal to 26 .6 degrees.
02:04
And finally, notice that if we take the square root of x squared plus y squared and divided by z, we have, let's write x squared, x squared is r squared times the sign squared of theta times the cosine squared of phi plus r squared times the sign squared of theta times the sign squared of phi divided by z, which is r times the cosine of theta.
02:41
So this is equal to the square root of r squared times the sign of theta squared, okay, because cosine of phi squared plus sine squared of phi is 1, divided by r times the cosine of theta, and this is equal to r, sine of phi divided by r cosine of phi...