The prefix 'co-' stands for complementary. Two complementary angles add up to 90°. The cosine of a angle is therefore the sine of its complementary angle, etc.

The prefix 'co-' stands for complementary. Two complementary angles add up to 90°. The cosine of a angle is therefore the sine of its complementary angle, etc. For the secant and tangent, it originates from the geometry of the unit circle. The first image in the article explains it well.