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# sin

Sine of fixed-point values

y = sin(theta)

## Description

y = sin(theta) returns the sine of fi input theta using a table-lookup algorithm.

## Input Arguments

 theta theta can be a real-valued, signed or unsigned scalar, vector, matrix, or N-dimensional array containing the fixed-point angle values in radians. Valid data types of theta are:fi singlefi double fi fixed-point with binary point scaling fi scaled double with binary point scaling

## Output Arguments

 y y is the sine of theta. y is a signed, fixed-point number in the range [-1,1]. It has a 16-bit word length and 15-bit fraction length (numerictype(1,16,15)) This sine calculation is accurate only to within the top 16 most-significant bits of the input.

## Examples

Calculate the sine of fixed-point input values.

```theta = fi([-pi/2,-pi/3,-pi/4 0, pi/4,pi/3,pi/2])

theta =

theta =

-1.5708  -1.0472  -0.7854  0  0.7854  1.0472  1.5708

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 14

y = sin(theta)

y =

-1.0000  -0.8661  -0.7072   0  0.7070  0.8659  0.9999

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 15
```

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### Sine

The sine of angle Θ is defined as

$\mathrm{sin}\left(\theta \right)=\frac{{e}^{i\theta }-{e}^{-i\theta }}{2i}$

### Algorithms

The sin function computes the sine of fixed-point input using an 8-bit lookup table as follows:

1. Cast the input to a 16-bit stored integer value, using the 16 most-significant bits.

2. Perform a modulo 2π, so the input is in the range [0,2π) radians.

3. Compute the table index, based on the 16-bit stored integer value, normalized to the full uint16 range.

4. Use the 8 most-significant bits to obtain the first value from the table.

5. Use the next-greater table value as the second value.

6. Use the 8 least-significant bits to interpolate between the first and second values, using nearest-neighbor linear interpolation.

### fimath Propagation Rules

The sin function ignores and discards any fimath attached to the input, theta. The output, y, is always associated with the default fimath.