# Trigonometric Function

Specified trigonometric function on input

• Library:
• Simulink / Math Operations

HDL Coder / Math Operations

• ## Description

The Trigonometric Function block performs common trigonometric functions and outputs the result in rad or rev.

### Supported Functions

You can select one of these functions from the Function parameter list.

FunctionDescriptionMathematical Expression MATLAB® Equivalent
`sin`

Sine of the input

`sin(u)`

`sin`
`cos`

Cosine of the input

`cos(u)`

`cos`
`tan`

Tangent of the input

`tan(u)`

`tan`
`asin`

Inverse sine of the input

`asin(u)`

`asin`
`acos`

Inverse cosine of the input

`acos(u)`

`acos`
`atan`

Inverse tangent of the input

`atan(u)`

`atan`
`atan2`

Four-quadrant inverse tangent of the input

`atan2(u)`

`atan2`
`sinh`

Hyperbolic sine of the input

`sinh(u)`

`sinh`
`cosh`

Hyperbolic cosine of the input

`cosh(u)`

`cosh`
`tanh`

Hyperbolic tangent of the input

`tanh(u)`

`tanh`
`asinh`

Inverse hyperbolic sine of the input

`asinh(u)`

`asinh`
`acosh`

Inverse hyperbolic cosine of the input

`acosh(u)`

`acosh`
`atanh`

Inverse hyperbolic tangent of the input

`atanh(u)`

`atanh`
`sincos`

Sine of the input; cosine of the input

`cos + jsin`

Complex exponential of the input

### CORDIC Approximation Method

CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations. For more information, see More About. The block input has further requirements.

For more information on when you set Function to `sin`, `cos`, `sincos`, or `cos + jsin` and set the Approximation method to `CORDIC`, see Port_1.

This table summarizes what happens for an invalid input.

Block UsageEffect of Invalid Input
Simulation modesAn error appears.
Generated codeUndefined behavior occurs. Avoid relying on undefined behavior for generated code.

### Lookup Approximation Method

For more information on when you set Function to `sin`, `cos`, `sincos`, or `cos + jsin` and set the Approximation method to `Lookup`, see Port_1.

## Ports

### Input

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Input specified as a scalar, vector, or matrix. The block accepts input signals of the following data types:

FunctionsInput Data Types
• `sin`

• `cos`

• `sincos`

• `cos + jsin`

• `atan2`

• Floating point

• Fixed point (only when Approximation method is `CORDIC`)

• `tan`

• `asin`

• `acos`

• `atan`

• `sinh`

• `cosh`

• `tanh`

• `asinh`

• `acosh`

• `atanh`

• Floating point

CORDIC approximation fixed-point type propagations:

Input Data TypeFunctionOutput Data Type

Fixed point, signed or unsigned

`sin`, `cos`, `sincos`, and ```cos + jsin```

`fixdt````(1, WL, WL - 2)``` where `WL` is the input word length

This fixed-point type provides the best precision for the CORDIC algorithm.

Fixed point, signed

`atan2`

`fixdt````(1, WL, WL – 3)```

Fixed point, unsigned

`atan2`

`fixdt````(1, WL, WL – 2)```

Lookup approximation fixed-point type propagations:

Input Data TypeFunctionOutput Data Type

Fixed point, signed

`sin`, `cos`, `sincos`, ```cos + jsin```, `atan2`

`fixdt````(1, WL, FL)```

Fixed point, unsigned

`sin`, `cos`, `sincos`, ```cos + jsin```, `atan2`

`fixdt````(1, WL - 1, FL)```

#### Dependencies

• When you set Function to `atan2`, the block shows two input ports. The first input (Port_1) is the y-axis or imaginary part of the function argument. The second input (Port_2) is the x-axis or real part of the function argument.

• You can use floating-point input signals when you set Approximation method to `None`, `CORDIC`, or `Lookup`. However, the block output data type depends on which of these approximation method options you choose.

Input Data TypeApproximation MethodOutput Data Type

Floating point

`None`

Depends on your selection for Output signal type. Options are `auto` (same data type as input), `real`, or `complex`.

Floating point

`CORDIC`

Same as input. Output signal type is not available when you use the CORDIC approximation method to compute the block output.

Floating point

`Lookup`

Same as input. Output signal type is not available when you use the Lookup approximation method to compute the block output.

For CORDIC and Lookup approximations:

• Input must be real for the `sin`, `cos`, `sincos`, `cos + jsin`, and `atan2` functions.

• Output is real for the `sin`, `cos`, `sincos`, and `atan2` functions.

• Output is complex for the `cos + jsin` function.

#### Limitations

• You can use fixed-point input signals only when Approximation method is set to `CORDIC` or `Lookup`. The CORDIC and Lookup approximations are available for the `sin`, `cos`, `sincos`, `cos + jsin`, and `atan2` functions.

• Complex input signals are supported for all functions in this block except `atan2`.

• When you set Approximation method to `Lookup`, the number of data points are limited by:

• ```smallEnoughNumDataPoints = 2(inputFractionLen-2)+1```

• ```bigEnoughFractionLen = log2(numberOfDataPoints - 1)+2```

where:

• smallEnoughNumDataPoints is the maximum number of data points represented by specified input fraction length, inputFractionLen.

• bigEnoughFractionLen is the minimum fraction length needed to represent specified number of data points, numberOfDataPoints.

• When you set Function to `sin`, `cos`, `sincos`, or `cos + jsin` and set the Approximation method to `CORDIC`, the block has these limitations:

• When you use signed fixed-point types, the input angle must fall within the range [–2π, 2π) rad.

• When you use unsigned fixed-point types, the input angle must fall within the range [0, 2π) rad.

When you set Function to `atan2` and the Approximation method to `CORDIC`, the block has these limitations:

• Inputs must be the same size, or at least one value must be a scalar value.

• Both inputs must have the same data type.

• When you use signed fixed-point types, the word length must be `126` or less.

• When you use unsigned fixed-point types, the word length must be `125` or less.

• When you set Function to `sin`, `cos`, `sincos`, or ```cos + jsin``` and set the Approximation method to `Lookup`, the block has these limitations.

• When you use signed fixed-point types, the input angle must fall within the range [-2π,2π] rad.

• When you use unsigned fixed-point types, the input angle must fall within the range [0,2π) rad.

• When you set Function to `atan2` and the Approximation method to `Lookup`, the block has these limitations:

• Inputs must be the same size, or at least one value must be a scalar value.

• Both inputs must have the same data type.

Data Types: `half` | `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `fixed point`

Input the x-axis or real part of the function argument for `atan2`. When you set Function to `atan2`, the block shows two input ports. The first input (Port_1) is the y-axis or imaginary part of the function argument. The second input (Port_2) is the x-axis or real part of the function argument. (See Port Location After Rotating or Flipping for a description of the port order for various block orientations.)

#### Dependencies

To enable this port, set Function to `atan2`.

#### Limitations

• Fixed-point input signals are supported only when you set Approximation method to `CORDIC` or `Lookup`.

Data Types: `half` | `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `fixed point`

### Output

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Result of applying the specified trigonometric function to one or more inputs in rad. Each function supports:

• Scalar operations

• Element-wise vector and matrix operations

Data Types: `half` | `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `fixed point`

Sine of the input signal, in rad and rev.

#### Dependencies

To enable this port, set Function to `sincos`.

#### Limitations

Fixed-point input signals are supported only when you set Approximation method to `CORDIC` or `Lookup`.

Data Types: `half` | `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `fixed point`

Cosine of the input signal, in rad and rev.

#### Dependencies

To enable this port, set Function to `sincos`.

#### Limitations

Fixed-point input signals are supported only when you set Approximation method to `CORDIC` or `Lookup`.

Data Types: `half` | `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `fixed point`

## Parameters

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### Algorithm

Specify the trigonometric function. The name of the function on the block icon changes to match your selection.

For more information on when you set Function to `sin`, `cos`, `sincos`, or `cos + jsin` and set the Approximation method to `CORDIC`, see Limitations.

#### Programmatic Use

 Block Parameter: `Operator` Type: character vector Values: ```'sin' | 'cos' | 'tan' | 'asin' | 'acos' | 'atan' | 'atan2' | 'sinh' | 'cosh' | 'tanh' | 'asinh' | 'acosh' | 'atanh' | 'sincos' | 'cos + jsin'``` Default: `'sin'`

Specify the type of approximation for computing output.

Approximation MethodData Types SupportedWhen to Use This Method
`None` (default)

Floating point

You want to use the default Taylor series algorithm.

`CORDIC`

Floating point and fixed point

You want a fast, approximate iterative calculation.

`Lookup`

Floating point and fixed point (double and single)

You want a fast, approximate lookup table implementation.

For more information on when you set Function to `sin`, `cos`, `sincos`, or `cos + jsin` and set the Approximation method to `CORDIC`, see Limitations.

#### Dependencies

• To enable this parameter, set Function to `sin`, `cos`, `sincos`, ```cos + jsin```, or `atan2`.

• To use fixed-point input signals, you must set Approximation method to `CORDIC` or `Lookup`.

• To enable the Table data type parameter, set this method to `Lookup`.

#### Programmatic Use

 Block Parameter: `ApproximationMethod` Type: character vector Values: `'None' | 'CORDIC' | 'Lookup'` Default: `'None'`

When an input falls between breakpoint values, the block interpolates the output value using neighboring breakpoints. For more information on interpolation methods, see Interpolation Methods.

#### Programmatic Use

 Block Parameter: `InterpMethod` Type: character vector Values: `'Linear point-slope' | 'Flat'` Default: `'Linear point-slope'`

Specify the number of iterations to perform the CORDIC algorithm. The default value is 11.

• When the block input uses a floating-point data type, the number of iterations can be a positive integer.

• When the block input is a fixed-point data type, the number of iterations cannot exceed the word length.

For example, if the block input is `fixdt(1,16,15)`, the word length is 16. In this case, the number of iterations cannot exceed 16.

#### Dependencies

To enable this parameter, you must set the Function and Approximation method parameters as follows:

• Set Function to `sin`, `cos`, `sincos`, ```cos + jsin```, or `atan2`.

• Set Approximation method to `CORDIC`.

#### Programmatic Use

 Block Parameter: `NumberOfIterations` Type: character vector Values: positive integer, less than or equal to word length of fixed-point input Default: `'11'`

Specify the angle unit for lookup method as `radian` or `revolution`.

#### Dependencies

To enable this parameter:

• Set Function to `sin`, `cos`, `sincos`, ```cos + jsin```, or `atan2`.

• Set to `Lookup`.

#### Programmatic Use

 Block Parameter: `AngleUnit` Type: character vector Values: `'radian' | 'revolution'` Default: `'radian'`

Specify the number of data points for lookup table as a scalar real number.

#### Dependencies

To enable this parameter:

• Set Function to `sin`, `cos`, `sincos`, ```cos + jsin```, or `atan2`.

• Set to `Lookup`.

#### Programmatic Use

 Block Parameter: `NumberOfDataPoints` Type: character vector Values: scalar Default: `'16'`

Specify the output signal type of the Trigonometric Function block as `auto`, `real`, or `complex`.

FunctionInput Signal TypeOutput Signal Type
AutoRealComplex
Any selection for the Function parameter realrealrealcomplex
complexcomplexerrorcomplex

#### Dependencies

Setting Approximation method to `CORDIC` disables this parameter.

Note

When Function is `atan2`, complex input signals are not supported for simulation or code generation.

#### Programmatic Use

 Block Parameter: `OutputSignalType` Type: character vector Values: `'auto' | 'real' | 'complex'` Default: `'auto'`

For `acos` and `asin`, select this check box to remove the protection against out-of-range inputs, which reduces redundancy.

• When you clear this check box, the protection is enabled. The block saturates out-of-range inputs to `1` or `-1` before any operation is performed. Generated code contains code to check for out-of-range input.

• When you select this check box, the protection is removed. The block performs all operations on the input value without any changes. Generated code does not contain code to check for the out-of-range input.

Enabling this check box can eliminate redundancy if the input is already in range.

#### Dependencies

Setting Function to `acos` and `asin` enables this parameter.

#### Programmatic Use

 Block Parameter: `RemoveProtectionAgainstOutOfRangeInput` Type: character vector Values: `'off' | 'on'` Default: `'off'`

Specify the sample time as a value other than `-1`. For more information, see Specify Sample Time.

#### Dependencies

This parameter is not visible unless it is explicitly set to a value other than `-1`. To learn more, see Blocks for Which Sample Time Is Not Recommended.

#### Programmatic Use

 Block Parameter: `SampleTime` Type: string scalar or character vector Default: `"-1"`

### Data Types

Data type for the lookup table, specified as:

• `Inherit: Inherit via input`

• `double`

• `single`

• `fixdt(1,16,0)`

• `<data type expression>`

For more information on setting data types, see Control Data Types of Signals.

#### Programmatic Use

 Block Parameter: `TableDataTypeStr` Type: string scalar or character vector Values: `Inherit: Inherit via input` | `single` | `double` | `fixdt(1,16,0)` | data type expression Default: `Inherit: Inherit via input`

Select how you would like to specify the data type properties of the Output data type. You can choose:

• `Inherit` — Lets you specify a rule for inheriting a data type, for example, ```Inherit: Inherit via internal rule```

• `Built in`— Lets you specify a built-in data type.

• `Fixed point` — Lets you specify the fixed-point attributes of the data type.

• `Expression` — Lets you specify an expression that evaluates to a valid data type, for example, `fixdt([],16,0)`

#### Dependencies

To enable this parameter, click >> at the Output data type parameter.

Specify the Signedness for the Output data type.

#### Dependencies

To enable this parameter, set Mode to `Fixed point`.

Specify the Scaling for the Output data type.

#### Dependencies

To enable this parameter, set Mode to `Fixed point`.

Select the data type override mode for this signal.

• `Inherit` — Inherits the data type override setting specified for the model.

• `Off` — Ignores the data type override setting specified for the model and uses the fixed-point data type you specify

For more information, see Specify Data Types Using Data Type Assistant in the Simulink® documentation.

#### Tips

The ability to turn off data type override for an individual data type provides greater control over the data types in your model when you apply data type override. For example, you can use this option to ensure that data types meet the requirements of downstream blocks regardless of the data type override setting.

#### Dependencies

To enable this parameter, click the button, and set Mode to `Built in` or ```Fixed point```.

Specify the bit size of the word that holds the quantized integer. For more information, see Specifying a Fixed-Point Data Type.

#### Dependencies

To enable this parameter, set Mode to `Fixed point`.

Specify fraction length for fixed-point data type as a positive or negative integer. For more information, see Specifying a Fixed-Point Data Type.

#### Dependencies

To enable this parameter, set:

• Mode to ```Fixed point```

• Scaling to ```Binary point```

## Block Characteristics

 Data Types `double` | `fixed pointa` | `half` | `integera` | `single` Direct Feedthrough `yes` Multidimensional Signals `yes` Variable-Size Signals `yes` Zero-Crossing Detection `no` a This block supports fixed-point and base integer data types for 'Approximation method' CORDIC.