arcsin, arccos, ... - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Conversions : Function : invtrig

arcsin, arccos, ...

The Inverse Trigonometric functions

arcsinh, arccosh, ...

The Inverse Hyperbolic functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

arcsin(x)    arccos(x)    arctan(x)

arcsec(x)    arccsc(x)    arccot(x)

arcsinh(x)   arccosh(x)   arctanh(x)

arcsech(x)   arccsch(x)   arccoth(x)

arctan(y, x)

Parameters

x

-

expression

y

-

expression

Description

• 

The arctrigonometric functions

arcsin

arccos

arctan

arcsec

arccsc

arccot

  

and archyperbolic functions

arcsinh

arccosh

arctanh

arcsech

arccsch

arccoth

  

compute inverses of the corresponding trigonometric and hyperbolic functions.

• 

The arctrigonometric and archyperbolic function are calculated in radians (1 radian = 180/π degrees).

• 

For information about expanding and simplifying trigonometric expressions, see expand, factor, combine/trig, and simplify/trig.

• 

As the trigonometric and hyperbolic functions are not invertible over the entire complex plane, or for many of them even over the real line, it is necessary to define a principal branch for each such inverse function.  This is done by restricting the forward function to a principal domain on which it is invertible, and taking that domain as the range of the inverse function.

  

This process necessarily results in discontinuities in the inverse functions, which can be taken to be along line segments (called branch cuts) in the real or imaginary axes.  There is choice involved with this process, and the choices can have far reaching mathematical consequences.  See invtrig/details for more information about Maple's choices for the branch cuts of these functions.

• 

For real arguments x, y, the two-argument function arctan(y, x), computes the principal value of the argument of the complex number x&plus;Iy, so π<arctany,xπ. This function is extended to complex arguments by the formula

arctany&comma;x&equals;Ilnx&plus;Iyx2&plus;y2

• 

Operator notation can also be used for the inverse trigonometric and hyperbolic functions.  For example, (sin@@(-1))(x) (which is equivalent to sin1x in 2-D math) evaluates to arcsinx.

Examples

arcsech1

0

(1)

arccsch1

ln1&plus;2

(2)

arccot0

12&pi;

(3)

sin1x

arcsinx

(4)

cosarccosx

x

(5)

sinarccosx

x2&plus;1

(6)

arctan1&comma;2

arctan12&plus;&pi;

(7)

evalf

2.677945045

(8)

arcsinh1.2&plus;3.4I

1.960545624&plus;1.218868917I

(9)

&DifferentialD;&DifferentialD;xarctanx

1x2&plus;1

(10)

Darcsech

z&rarr;1z21z11z&plus;1

(11)

&DifferentialD;&DifferentialD;xarcsechx

1x21x11x&plus;1

(12)

&int;arcsinhx&DifferentialD;x

xarcsinhxx2&plus;1

(13)

convertarccoshx&comma;ln

lnx&plus;x&plus;1x1

(14)

See Also

@@

argument

convert

initialfunctions

invtrig/details

polar

RealDomain

trig

type/arctrig

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam