What is a cofunction?

If f(A) = g(B) wherever A and B are complementary angles, a function f is a cofunction of a function g in mathematics. This is a common definition for trigonometric functions. Edmund Gunter's contains the prefix "co-". Sine and cosine are examples of cofunctions (hence the "co" in "cosine"). Secant and cosecant are the same as tangent and cotangent. This is also related to versine, coversine, vercosine, covercosine, haversine, hacoversine, havercosine, hacovercosine, exsecant and excosecant.

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Cofunction identities - an example

To fully simplify the equation, use cofunction identities. Determine which cofunction identities are required and use them as needed. To simplify fully, utilize other well-known formulae and trigonometric identities, such as reciprocal or Pythagorean identities.

  • Cos (π/2−x) csc x
  • Sin x = cos (π/2−x) sin x = cos (π/2−x)
  • Cos (π/2−x) csc x = sin x csc x
  • Csc x = 1 sin x csc x = 1 sin x
  • Sin x csc x = sin x (1/sin x) = 1
  • Cos (π/2−x) csc x = 1
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What is the cofunction of tan and cot?

Tangent and cotangent are complementary cofunctions.

  • cos (π/2 – u) = sin (u)
  • sin (π/2 – u) = cos (u)

A tangent percentage of a right triangle's opposing side to its neighbouring side. On the other hand, the cotangent is the ratio of adjacent and opposing sides of a right triangle. We can define the tangent of x as the sine divided by the cosine. The formula is tanx = sinx / cox. And also, we can define the contangent as the cosine that is divided by the sine. Formula is cotx = cosx / sinx.

What is the cofunction of sin and cos?

In mathematics, the trigonometric functions of an angle are sine and cosine. In the context of a right triangle, the sine and cosine of an acute angle are defined as follows: the sine is the proportion of the length of the opposing side to the length of the triangle's longest side (the hypotenuse) for the given angle, and the cosine is the proportion of the length of the adjacent leg to the hypotenuse. Sine and cosine are complementary functions.

  • tan (π/2 – u) = cot (u)
  • cot (π/2 – u) = tan (u)

What is the cofunction of csc and sec?

The term 'sec' stands for secant. Because the secant function is the cosine function's inverse, anytime the cosine function is equal to zero. The secant function goes to infinity (0). Cosecant, often known as cosec or csc, is one of the six trigonometric ratios. In a right triangle, the cosecant formula is the length of the hypotenuse divided by the length of the opposite side. Secant and cosecant are complements and cofunctions.

  • sec (π/2−u) = csc (u)
  • csc (π/2−u) = sec (u)