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This question already has an answer here:

How to Move points according to distance and azimuth ?

marked as duplicate by Vince, Farid Cheraghi, Get Spatial, Aaron Oct 6 '15 at 18:00

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    Please edit your question to contain several paragraphs which detail: The operating system(s) and software available (name and version), a description of the data being moved, the programming language(s) available, and some indication of the work you have done to solve the problem yourself (if this includes code, you should provide it). Further details on what is expected can be found by taking the Tour and reviewing the Help pages. – Vince Oct 6 '15 at 17:29
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The difference is really between the projected and geographic coordinates. Let me explain the case if you have projected coordinates - which is simpler:

original coordinates: x1,y1 (x:abscissa, y: ordinate)
distance: d
azimuth: a

x2 = x1 + d*sin(a)
y2 = y1 + d*cos(a)

However, here are the formulas to calculate coordinates on the sphere based on the bearing and distance.

  • I think you meant to flip sin() and cos() -- SOH-CAH-TOA - sine is the Y component (opposite), cosine the X (adjacent), though it depends on how you calculate azimuth (which should be in radians for computers) – Vince Oct 7 '15 at 3:30
  • @Vince: I don't think so. Note that "a" is azimuth (an angle from the vertical, y axis) not the angle from the x-axis. – Matej Oct 7 '15 at 17:48

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