Calculates trigonometric values.

## Description

### Primary functions

The **Cos** function returns the cosine of its argument, an angle specified in radians.

The **Cot** function returns the cotangent of its argument, an angle specified in radians.

The **Sin** function returns the sine of its argument, an angle specified in radians.

The **Tan** function returns the tangent of its argument, an angle specified in radians.

### Inverse functions

The **Acos** function returns the arccosine, or inverse cosine, of its argument. The arccosine is the angle whose cosine is the argument. The returned angle is given in radians in the range 0 (zero) to π.

The **Acot** function returns the principal value of the arccotangent, or inverse cotangent, of its argument. The returned angle is given in radians in the range 0 (zero) to π.

The **Asin** function returns the arcsine, or inverse sine, of its argument. The arcsine is the angle whose sine is the argument. The returned angle is given in radians in the range -π/2 to π/2.

The **Atan** function returns the arctangent, or inverse tangent, of its argument. The arctangent is the angle whose tangent is the argument. The returned angle is given in radians in the range -π/2 to π/2.

The **Atan2** function returns the arctangent, or inverse tangent, of the specified *x* and *y* coordinates as arguments. The arctangent is the angle from the *x*-axis to a line that contains the origin (0, 0) and a point with coordinates (*x*, *y*). The angle is given in radians between -π and π, excluding -π. A positive result represents a counterclockwise angle from the *x*-axis; a negative result represents a clockwise angle. **Atan2( a, b )** equals

**Atan(**, except that

*b*/*a*)**can equal 0 (zero) with the**

*a***Atan2**function.

### Helper functions

The **Degrees** function converts radians to degrees. π radians equals 180 degrees.

The **Pi** function returns the transcendental number π, which begins 3.141592...

The **Radians** function converts degrees to radians.

### Notes

If you pass a single number to these functions, the return value is a single result. If you pass a single-column table that contains numbers, the return value is a single-column table of results, one result for each record in the argument's table. If you have a multi-column table, you can shape it into a single-column table, as working with tables describes.

If an argument would result in an undefined value, the result is *blank*. This can happen, for example, when using inverse functions with arguments that are out of range.

## Syntax

### Primary Functions

**Cos**( *Radians* )**Cot**( *Radians* )**Sin**( *Radians* )**Tan**( *Radians* )

*Radians*- Required. Angle to operate on.

**Cos**( *SingleColumnTable* )**Cot**( *SingleColumnTable* )**Sin**( *SingleColumnTable* )**Tan**( *SingleColumnTable* )

*SingleColumnTable*- Required. A single-column table of angles to operate on.

### Inverse Functions

**Acos**( *Number* )**Acot**( *Number* )**Asin**( *Number* )**Atan**( *Number* )

*Number*- Required. Number to operate on.

**Acos**( *SingleColumnTable* )**Acot**( *SingleColumnTable* )**Asin**( *SingleColumnTable* )**Atan**( *SingleColumnTable* )

*SingleColumnTable*- Required. A single-column table of numbers to operate on.

**Atan2**( *X*, *Y* )

*X*- Required.*X*-axis coordinate.*Y*- Required.*Y*-axis coordinate.

### Helper Functions

**Degrees**( *Radians* )

*Radians*- Required. Angle in radians to convert to degrees.

**Pi**()

**Radians**( *Degrees* )

*Degrees*- Required. Angle in degrees to convert to radians.

## Examples

### Single number

Formula | Description | Result |

Cos( 1.047197 ) | Returns the cosine of 1.047197 radians or 60 degrees. | 0.5 |

Cot( Pi()/4 ) | Returns the cotangent of 0.785398... radians or 45 degrees. | 1 |

Sin( Pi()/2 ) | Returns the sine of 1.570796... radians or 90 degrees. | 1 |

Tan( Radians(60) ) | Returns the tangent of 1.047197... radians or 60 degrees. | 1.732050... |

Acos( 0.5 ) | Returns the arccosine of 0.5, in radians. | 1.047197... |

Acot( 1 ) | Returns the arccotangent of 1, in radians. | 0.785398... |

Asin( 1 ) | Returns the arcsine of 1, in radians. | 1.570796... |

Atan( 1.732050 ) | Returns the arctangent of 1.732050, in radians. | 1.047197... |

Atan2( 5, 3 ) | Returns the arctangent of the angle from the x-axis of the line that contains the origin (0,0) and the coordinate (5,3), which is approximately 31 degrees. | 0.540419... |

Atan2( 4, 4 ) | Returns the arctangent of the angle from the x-axis of the line that contains the origin (0,0) and the coordinate (4,4), which is exactly π/4 radians or 45 degrees. | 0.785398... |

Degrees( 1.047197 ) | Returns the equivalent number of degrees for 1.047197 radians. | 60 |

Pi() | Returns the transcendental number π. | 3.141592... |

Radians( 15 ) | Returns the equivalent number of radians for 15 degrees. | 0.261799... |

### Single-column table

The examples in this section use a data source that's named **ValueTable** and that contains the following data. The last record in the table is π/2 radians or 90 degrees.

Formula | Description | Result |

Cos( ValueTable ) | Returns the cosine of each number in the table. | |

Cot( ValueTable ) | Returns the cotangent of each number in the table. | |

Sin( ValueTable ) | Returns the sine of each number in the table. | |

Tan( ValueTable ) | Returns the tangent of each number in the table. | |

Acos( ValueTable ) | Returns the arccosine of each number in the table. | |

Acot( ValueTable ) | Returns the arccotangent of each number in the table. | |

Asin( ValueTable ) | Returns the arcsine of each number in the table. | |

Atan( ValueTable ) | Returns the arctangent of each number in the table. | |

Degrees( ValueTable ) | Returns the equivalent number of degrees for each number in the table, assumed to be angles in radians. | |

Radians( ValueTable ) | Returns the equivalent number of radians for each number in the table, assumed to be angles in degrees. |