TRIGONOMETRIC COFUNCTION Meaning and
Definition
-
A trigonometric cofunction refers to the relationship between two complementary trigonometric functions. Complementary angles are two angles whose sum is equal to a right angle, which is 90 degrees (π/2 radians). In trigonometry, there are six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).
The cofunctions of these trigonometric functions are defined as follows:
1. The sine (sin) and cosine (cos) are cofunctions of each other. The sine of an angle is defined as the ratio of the length of the side opposite the angle to the hypotenuse of a right triangle, while the cosine is the ratio of the length of the adjacent side to the hypotenuse.
2. The tangent (tan) and cotangent (cot) are cofunctions of each other. The tangent of an angle is defined as the ratio of the sine to the cosine of that angle, while the cotangent is the reciprocal of the tangent, or the ratio of the cosine to the sine.
3. The cosecant (csc) and secant (sec) are cofunctions of each other. The cosecant of an angle is defined as the reciprocal of the sine, or the ratio of the hypotenuse to the opposite side, while the secant is the reciprocal of the cosine, or the ratio of the hypotenuse to the adjacent side.
These trigonometric cofunctions are useful in solving trigonometric equations and identifying correspondences between different angles in a triangle or on the unit circle.
Etymology of TRIGONOMETRIC COFUNCTION
The word "trigonometric" comes from the Greek words "trigonon" meaning "triangle" and "metron" meaning "measure". This reflects the fact that trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles.
The term "cofunction" is a combination of the prefix "co-" meaning "together" or "mutual", and the word "function". In mathematics, a function is a relation between two sets, where each element of the first set is associated with exactly one element of the second set. The term "cofunction" specifically refers to two functions that have a complementary relationship or are inverses of each other.
Therefore, the term "trigonometric cofunction" refers to the complementary relationship between trigonometric functions, such as sine and cosine, or tangent and cotangent.
