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# Cofunction Calculator

To use cofunction calculator, select the function, enter the angle, and click calculate

Table of Contents:

## Cofunction Calculator

Cofunction calculator is used to calculate the cofunctions values of trigonometric angles. This Co-function calculator provides a Step-by-Step solution for every suitable input.

## What is the Cofunction?

A cofunction in trigonometry is a connection between two trigonometric functions that are connected by a complementary angle. In another way say that the cofunction of an angle is the trigonometric function of its complement. The angle is inputted as the sum of 90 degrees or π/2 radians for trigonometric angles.

**Formulas of cofunction**

Function | Cofunction identity |

sine | sin(x) = cos(90° - x) |

cosine | cos(x) = sin(90° - x) |

tangent | tan(x) = cot(90° - x) |

cotangent | cot(x) = tan(90° - x) |

Secant | sec(x) = csc(90° - x) |

cosecant | csc(x) = sec(90° - x) |

## How to calculate cofunction?

Here we explain a few examples of cofunctions of different trigonometric functions.

**Example 1:**

If the Angle is “270^{o}” then find the Cofunction value of “sin(θ)” in terms of “**degree”.**

**Solution:**

**Step 1:** Write the given data from the problem.

θ = 270^{o}, Cofunction of sin(θ) =?

**Step 2:** Write the formula of Cofunction of sin(θ).

sin(θ) = cos(90 − θ)

**Step 3:** Now put the values of the given data in the above expression.

sin(270^{o}) = cos(90 − 270^{o})

sin(270^{o}) = cos(-180^{0})

sin(270^{o}) = cos(180^{0}) as cos(-x) = cos(x)

sin(270^{o}) = -1.0

**Example 2:**

If the Angle is “180^{o}” then find the Cofunction of “cos(θ)” in terms of “**degree”.**

**Solution:**

**Step 1:** Write the given data from the problem.

θ = 180^{o}, Cofunction of cos(θ) =?

**Step 2:** Write the formula of cofunction of cos(θ).

cos(θ)= sin(90 − θ)

**Step 3:** Now put the values of the given data in the above expression.

cos(180^{o}) = sin(90 − 180^{0})

cos(180^{o}) = sin(− 90^{0})

cos(180^{o}) = - sin(90^{0}) as sin(-x) = - sin(x)

**cos(180 ^{o}) = - 1.0**

**Example 3:**

If the Angle is “180^{0}” then find the Cofunction of “cos(θ)” in terms of “**radians”.**

**Solution:**

**Step 1:** Write the given data from the problem.

θ = 180^{o}, Cofunction of cos(θ) =?

**Step 2:** Write the formula of cofunction of cos(θ).

cos(θ)= sin(π/2 − θ)

**Step 3:** Now put the values of the given data in the above expression.

cos(180^{o})= sin([π/2] − 180^{0})

cos(180^{o})= sin(−178.42920367)

cos(180^{o})= - sin(178.42920367)

**cos(180**^{o}**)= - 0.5985**