**COS Function in Microsoft Excel**

**Part 1: Introduce**

π **Definition** The COS function in Microsoft Excel returns the cosine of a given angle.

π **Purpose** The main Purpose of the COS function is to compute the cosine value of a specified angle in radians.

π **Syntax & Arguments**

`COS(number)`

**Number**: Required. The angle in radians for which you want the cosine.

π **Explain the Arguments in the function**

**Number**: This is the angle in radians for determining the cosine value.

π **Return value** The function returns the cosine value of the provided angle in radians.

π **Remarks** If the angle is in degrees, you can multiply the angle by `PI()/180`

or use the `RADIANS`

function to convert the angle to radians.

**Part 2: Examples**

π **Example 1**

**Purpose of example**: Calculate the cosine value of an angle in radians.**Data sheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Angle | Formula | Result |

2 | 1.047 | =COS(A2) | 0.500171 |

**Explanation**: This example demonstrates how to determine the cosine value of 1.047 radians using the COS function.

π **Example 2**

**Purpose of example**: Convert degrees to radians and find the cosine value.**Data sheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Degrees | Formula | Result |

2 | 60 | =COS(A2*PI()/180) | 0.5 |

**Explanation**: Here, the angle is converted from degrees to radians using the formula`A2*PI()/180`

, then its cosine value is computed.

π **Example 3**

**Purpose of example**: Use the RADIANS function to convert degrees to radians and compute the cosine value.**Data sheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Degrees | Formula | Result |

2 | 60 | =COS(RADIANS(A2)) | 0.5 |

**Explanation**: In this scenario, the`RADIANS`

function transforms the angle in cell A2 from degrees to radians. Subsequently, the cosine value is calculated.

π **Example 4**

**Purpose of example**: Determine the cosine value of a slight angle in radians.**Data sheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Angle | Formula | Result |

2 | 0.523 | =COS(A2) | 0.866025 |

**Explanation**: This example showcases how to compute the cosine value for a smaller angle in radians.

π **Example 5**

**Purpose of example**: Calculate the cosine value of a negative angle in radians.**Data sheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Angle | Formula | Result |

2 | -1.047 | =COS(A2) | -0.500171 |

**Explanation**: Negative angles in radians can also be used with the COS function. This example illustrates finding the cosine value for a negative slope in radians.

π **Example 6: COS with IF Function**

**Purpose of example**: Determine if the cosine value of a hook is positive or negative.**Data sheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Angle | Formula | Result |

2 | 1.047 | =IF(COS(A2)>0,”Positive”,”Negative”) | Positive |

**Explanation**: This example checks if the cosine value of the angle in cell A2 is positive. If it is, it returns “Positive”; otherwise, it replaces “Negative”.

π **Example 7: COS with SUM Function**

**Purpose of example**: Sum the cosine values of multiple angles.**Data sheet and formulas**:

A | B | C | D | |
---|---|---|---|---|

1 | Angle | Formula | Result | Total |

2 | 1.047 | =COS(A2) | 0.500171 | |

3 | 0.523 | =COS(A3) | 0.866025 | |

4 | =SUM(C2:C3) |

**Explanation**: The cosine values of the angles in cells A2 and A3 are calculated and summed up in cell D4.

π **Example 8: COS with VLOOKUP Function**

**Purpose of example**: Look up the cosine value of a given angle from a table.**Data sheet and formulas**:

A | B | C | D | |
---|---|---|---|---|

1 | Angle | Cosine | Lookup | |

2 | 1.047 | 0.500171 | 1.047 | |

3 | 0.523 | 0.866025 | ||

4 | =VLOOKUP(D2,A2:B3,2,FALSE) |

**Explanation**: The cosine value of the angle in cell D2 is looked up from the table in columns A and B.

π **Example 9: COS with AVERAGE Function**

**Purpose of example**: Average the cosine values of multiple angles.**Data sheet and formulas**:

A | B | C | D | |
---|---|---|---|---|

1 | Angle | Formula | Result | Average |

2 | 1.047 | =COS(A2) | 0.500171 | |

3 | 0.523 | =COS(A3) | 0.866025 | |

4 | =AVERAGE(C2:C3) |

**Explanation**: The cosine values of the angles in cells A2 and A3 are calculated and then averaged in cell D4.

π **Example 10: COS with MAX Function**

**Purpose of example**: Find the maximum cosine value from a set of angles.**Data sheet and formulas**:

A | B | C | D | |
---|---|---|---|---|

1 | Angle | Formula | Result | Max |

2 | 1.047 | =COS(A2) | 0.500171 | |

3 | 0.523 | =COS(A3) | 0.866025 | |

4 | =MAX(C2:C3) |

**Explanation**: The maximum cosine value between the angles in cells A2 and A3 is determined in cell D4.

π **Example 11: COS with MIN Function**

**Purpose of example**: Find the minimum cosine value from a set of angles.**Data sheet and formulas**:

A | B | C | D | |
---|---|---|---|---|

1 | Angle | Formula | Result | Min |

2 | 1.047 | =COS(A2) | 0.500171 | |

3 | 0.523 | =COS(A3) | 0.866025 | |

4 | =MIN(C2:C3) |

**Explanation**: The minimum cosine value between the angles in cells A2 and A3 is determined in cell D4.

π **Example 12: COS with ROUND Function**

**Purpose of example**: Round the cosine value of an angle to two decimal places.**Data sheet and formulas**:

A | B | C | |
---|---|---|---|

1 | Angle | Formula | Result |

2 | 1.047 | =ROUND(COS(A2),2) | 0.50 |

**Explanation**: The cosine value of the angle in cell A2 is rounded to two decimal places using the ROUND function.

**Β **

**Part 3: Tips and tricks**

- Always ensure that the angle is in radians when using the COS function. If you have the angle in degrees, convert it to radians first.
- The COS function can handle both positive and negative angles.
- For precise calculations, especially in trigonometry, it’s essential to use the
`RADIANS`

function for converting degrees to radians. - Remember that the cosine value will always be between -1 and 1.
- Combining the COS function with other trigonometric functions can help solve complex mathematical problems in Excel.