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# cos

Cosine of fi object in radians

## Description

example

Y = cos(X) returns the cosine for each element of fi input X using an 8-bit lookup table algorithm.

## Examples

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Calculate the cosine of fixed-point input values.

X = fi([0,pi/4,pi/3,pi/2,(2*pi)/3,(3*pi)/4,pi])
X =
0    0.7854    1.0472    1.5708    2.0944    2.3562    3.1416

DataTypeMode: Fixed-point: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 13
Y = cos(X)
Y =
1.0000    0.7072    0.4999    0.0001   -0.4999   -0.7070   -1.0000

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

## Input Arguments

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Input angle in radians, specified as a scalar, vector, matrix, or multidimensional array.

X can be a real-valued, signed or unsigned:

• fi single

• fi double

• fi fixed-point with binary-point scaling

• fi scaled double with binary-point scaling

Example: X = fi([pi pi/6],1,8);

Data Types: fi

## Output Arguments

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Cosine of input angle, returned as a real-valued fi scalar, vector, matrix, or multidimensional array.

## More About

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### Cosine

The cosine of angle Θ is defined as

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

## Algorithms

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

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

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

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 cos function ignores and discards any fimath attached to the input, X. The output, Y, is always associated with the default fimath.

## Version History

Introduced in R2012a