That's FALSE.
It's sine and cosecant that are reciprocals, as are cosine and secant, as well as tangent and cotangent.
The "co" or complementary functions are their corresponding non-complementary function applied to the complementary angle: cos(x) = sin(90-x), that kind of thing.
The non-co functions sine, secant and tangent all increase with increasing angle in the first quadrant. The co functions all decrease.
Since when sine increases its reciprocal decreases, its reciprocal must be one of the co functions, and of course it's cosecant.
