# acos

Symbolic inverse cosine function

## Syntax

``acos(X)``

## Description

example

````acos(X)` returns the inverse cosine function (arccosine function) of `X`. All angles are in radians. For real values of `X` in the interval `[-1,1]`, `acos(x)` returns the values in the interval `[0,pi]`.For real values of `X` outside the interval `[-1,1]` and for complex values of `X`, `acos(X)` returns complex values with the real parts in the interval `[0,pi]`. ```

## Examples

### Inverse Cosine Function for Numeric and Symbolic Arguments

Depending on its arguments, `acos` returns floating-point or exact symbolic results.

Compute the inverse cosine function for these numbers. Because these numbers are not symbolic objects, `acos` returns floating-point results.

`A = acos([-1, -1/3, -1/2, 1/4, 1/2, sqrt(3)/2, 1])`
```A = 3.1416 1.9106 2.0944 1.3181 1.0472 0.5236 0```

Compute the inverse cosine function for the numbers converted to symbolic objects. For many symbolic (exact) numbers, `acos` returns unresolved symbolic calls.

`symA = acos(sym([-1, -1/3, -1/2, 1/4, 1/2, sqrt(3)/2, 1]))`
```symA = [ pi, pi - acos(1/3), (2*pi)/3, acos(1/4), pi/3, pi/6, 0]```

Use `vpa` to approximate symbolic results with floating-point numbers:

`vpa(symA)`
```ans = [ 3.1415926535897932384626433832795,... 1.9106332362490185563277142050315,... 2.0943951023931954923084289221863,... 1.318116071652817965745664254646,... 1.0471975511965977461542144610932,... 0.52359877559829887307710723054658,... 0]```

### Plot Inverse Cosine Function

Plot the inverse cosine function on the interval from -1 to 1.

```syms x fplot(acos(x),[-1 1]) grid on``` ### Handle Expressions Containing Inverse Cosine Function

Many functions, such as `diff`, `int`, `taylor`, and `rewrite`, can handle expressions containing `acos`.

Find the first and second derivatives of the inverse cosine function:

```syms x diff(acos(x), x) diff(acos(x), x, x)```
```ans = -1/(1 - x^2)^(1/2) ans = -x/(1 - x^2)^(3/2)```

Find the indefinite integral of the inverse cosine function:

`int(acos(x), x)`
```ans = x*acos(x) - (1 - x^2)^(1/2)```

Find the Taylor series expansion of `acos(x)`:

`taylor(acos(x), x)`
```ans = - (3*x^5)/40 - x^3/6 - x + pi/2```

Rewrite the inverse cosine function in terms of the natural logarithm:

`rewrite(acos(x), 'log')`
```ans = -log(x + (1 - x^2)^(1/2)*1i)*1i```

## Input Arguments

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Input, specified as a symbolic number, variable, expression, or function, or as a vector or matrix of symbolic numbers, variables, expressions, or functions.