What does the colon in Tikz coordinates mean?

Question

\draw (0,0) -- (60:.75cm) arc (60:180:.75cm);

What does the colon in (60:.75cm) mean? Normally, I'd define a normal point there.

Answer 1

The colon signifies that polar coordinates are being used. (60:.75cm) means the point that is at an angle of 60° and a distance of 0.75cm from the origin.

In the TikZ/PGF manual this is mentioned in section 13.2 Coordinate Systems, p 125:

The implicit form for canvas polar coordinates is the following: you specify the angle and the distance, separated by a colon as in (30:1cm).

This also holds for other coordinate systems like xyz polar. Alternatively, if you're not interested in this shorthand notation, TikZ also provides

\pgfpointpolar{<degree>}{<x-radius>/<y-radius>}

where <y-radius> is optional. See section 70 Specifying Coordinates (p 571) of the documentation.