Cosine's reciprocal (6)
I believe the answer is:
secant
'cosine's reciprocal' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for secant that I've seen before include "Line that intersects a curve at two or more points" , "Line that intercepts a curve" , "Cutting line (geometry)" , "Ratio of the hypotenuse to the adjacent side in a right-angled triangle" , "triangular relationship" .)