How this calculation works
Convert two pointing angles to the three components of a unit direction vector.
u=(cos(e)cos(a), cos(e)sin(a), sin(e))A worked example
An azimuth of 60° on the xy plane gives (0.5, √3/2, 0).
Good to know
Azimuth starts at the positive x axis. A compass convention may measure from a different axis.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Convert two pointing angles to the three components of a unit direction vector.
The primary result is labeled “X direction cosine”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Azimuth starts at the positive x axis. A compass convention may measure from a different axis.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
An azimuth of 60° on the xy plane gives (0.5, √3/2, 0).
Which rule does this calculator apply?
u=(cos(e)cos(a), cos(e)sin(a), sin(e))