I've been looking around for a specific formula to create a Unit Vector representing the direction created by a given Pitch/Yaw.

The formula I see commonly is:

Where v is the resulting unit vector, y is the yaw and p is the pitch.Code:v = [ cos(y)*cos(p), sin(y), cos(y)*sin(p) ]

However, when plugging in the most simple test angles to make sure it's legitimate, I get a discrepancy. For example:

Obviously the unit vector [0.5, 0.7071, 0.5] does not represent the pitch/yaw of 45.0/45.0 because any vector with orientations of 45 have matching values (i.e [3, 3, 3]).Code:pitch = 45.0 yaw = 45.0 v = [ cos(45.0)*cos(45.0), sin(45.0), cos(45.0)*sin(45.0) ] v = [ 0.7071*0.7071, 0.7071, 0.7071*0.7071 ] v = [0.5, 0.7071, 0.5]

Is there a standard formula to convert Pitch/Yaw values into a Unit Vector? Am I doing something wrong with the formula above?