COFUNCTION Meaning and
Definition
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Cofunction is a mathematical term that refers to a relationship between trigonometric functions. Specifically, it describes two trigonometric functions that have equal values when their angles are complementary. In other words, if two angles are complementary, the cofunction of one angle is equal to the trigonometric function of the other angle.
For example, consider the sine and cosine functions. The sine of an angle (θ) is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse in a right triangle. The cosine of the same angle (θ) is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. In this case, the sine and cosine functions are cofunctions of each other.
The cofunction relationship can also be extended to other trigonometric functions, such as tangent and cotangent, secant and cosecant. For instance, the tangent of an angle (θ) is defined as the ratio of the length of the opposite side to the adjacent side in a right triangle. The cotangent of the same angle (θ) is defined as the ratio of the length of the adjacent side to the opposite side. Thus, tangent and cotangent are cofunctions of each other.
Understanding the concept of cofunctions is crucial in trigonometry as it helps simplify and solve various trigonometric equations and identities. Knowledge of cofunctions allows one to quickly determine the value of one trigonometric function when the value of its cofunction is known, and vice versa.
Common Misspellings for COFUNCTION
- confuction
- xofunction
- vofunction
- fofunction
- dofunction
- cifunction
- ckfunction
- clfunction
- cpfunction
- c0function
- c9function
- codunction
- cocunction
- covunction
- cogunction
- cotunction
- corunction
- cofynction
- cofhnction
- cofjnction
Etymology of COFUNCTION
The word "cofunction" is derived from the combination of two terms: "co-" and "function".
The prefix "co-" originates from the Latin prefix "com-" meaning "together" or "with". It conveys the idea of collaboration or joint action. In mathematics, the prefix "-co" is often used to indicate a complement or counterpart.
The term "function" comes from the Latin word "functio", which means "performance" or "execution". It refers to a mathematical relation that associates elements between two sets. Functions are fundamental in mathematics as they describe the relationship between inputs and outputs.
Therefore, "cofunction" combines the prefix "co-" and the word "function" to indicate a counterpart or complementary function that works in relation to another function. In trigonometry, for example, the cofunction of an angle is the function of its complementary angle.
