Why sec and cosec are called sec and cosec

secant

Sec θ is called sec θ because geometrically, in the diagram above, it is the “secant” line (“secant”, from a Latin word meaning cut, is a line from a point cutting through a circled).

cosecant

Cosec θ is called cosec θ because geometrically, in the diagram, it is another “secant” line, and, historically, people thought of the secant defined as for “secant” (from a vertical tangent) as primary and the secant defined as for “cosecant” (from a horizontal tangent) as secondary.