BUILT-IN MATHEMATICA SYMBOL

ArcCos

ArcCos[z]
gives the arc cosine

of the complex number

.

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

All results are given in radians.

For real between and , the results are always in the range to .

For certain special arguments, ArcCos automatically evaluates to exact values.

ArcCos can be evaluated to arbitrary numerical precision.

ArcCos automatically threads over lists.

ArcCos[z] has branch cut discontinuities in the complex plane running from to and to .

EXAMPLES

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Basic Examples (3)

Results are in radians:

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In[1]:=

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In[1]:=

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Scope (6)

Evaluate numerically:

Evaluate for complex arguments:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

The precision of the output can be much less than the precision of the input:

Simple exact values are generated automatically:

ArcCos threads element-wise over lists and matrices:

TraditionalForm formatting:

Generalizations & Extensions (6)

ArcCos can deal with real-valued intervals from

:

Infinite arguments give symbolic results:

ArcCos can be applied to power series:

Find series expansions at branch points and branch cuts:

ArcCos threads over explicit lists as well as over sparse arrays:

ArcCos is a numerical function:

Applications (3)

Plot the real and imaginary part of ArcCos:

Plot the Riemann surface of ArcCos:

Find the angle between two vectors:

Properties & Relations (9)

Compose with the inverse function:

Use PowerExpand to disregard multivaluedness of the ArcCos:

Alternatively, evaluate under additional assumptions:

Use TrigToExp to express ArcCos through logarithms and square roots:

This shows the branch cuts of the ArcCos function:

Expand assuming real variables:

Solve an inverse trigonometric equation:

Solve for zeros:

Integrals:

Laplace transforms:

ArcCos is automatically returned as a special case for various mathematical functions:

Possible Issues (3)

Generically

:

On branch cuts, machine-precision inputs can give numerically wrong answers:

In traditional form, parentheses are needed around the argument:

Neat Examples (2)

Nested integrals: