move a point up and down along a sphere I have a problem where i have a sphere and 1 point that can be anywhere on that sphere's surface. The Sphere is at the center point (0,0,0).
I now need to get 2 new points, 1 just a little below the and another little above this in reference to the Y axis. If needed or simpler to solve, the points can be about 15º above and below the original point, this viewing the movement on a 2D circle.
Thank you in advance for any given help. 
EDIT:
This is to be used on a world globe where the selected point will never be on the top or bottom.
EDIT:
I'm using the latitude and longitude suggested by rlgordonma and user1551
what I'm doing is adding and subtracting a fixed value to ϕ
These 2 apear correctly, at least they apear to look in place: 
The original point is in the middle of the 2 bars.
The sphere has R=1 all the coords i'm putting here are rounded because they are to big (computer processed)

coord: (0.77, 0.62, 0,11) 

coord: (0.93, -0.65, 0.019)
these don't:

coord: (-0.15, 0.59, 0.79)

coord: (-0.33, 0.73, -0.815)
there are other occasions for both but i didn't want to put all here.
calcs:
    R = 1
    φ = arctan(y/x)
    θ = arccos(z/1)
//to move up only one is used
    φ = φ + π/50
//to move down only one is used
    φ = φ - π/50

    (x,y,z)=(sinθ cosφ, sinθ sinφ, cosθ)


The conversion between Cartesian and spherical coordinates is 
$$ (x,y,z) = (R \sin{\theta} \cos {\phi},R \sin{\theta} \sin {\phi}, R \cos{\theta})$$
where $R$ is the radius of the earth/sphere, $\theta = $  $+90^{\circ}$- latitude, and $\phi=$ longitude.
