See also:

HEAD

 

 

TAN

Analytic function

Type:

Description:

Tangent Analytic Function: Returns the tangent of the argument.

 

For real arguments, the current angle mode determines the number’s interpretation as an angle,

 

unless the angular units are specified.

 

For a real argument that is an odd-integer multiple of 90 in Degrees mode, an Infinite Result

 

exception occurs. If flag –22 is set (no error), the sign of the result (MAXR) matches that of the

 

argument.

 

For complex arguments:

 

tan(x + iy) = (------------------------------------------------------------------------------sinx)( cosx) + i( sinhy)( coshy)

 

sinh2y + cos2x

 

If the argument for TAN is a unit object, then the specified angular unit overrides the angle mode

 

to determine the result. Integration and differentiation, on the other hand, always observe the

 

angle mode. Therefore, to correctly integrate or differentiate expressions containing TAN with a

 

unit object, the angle mode must be set to Radians (since this is a “neutral” mode).

Access:

U

Flags: Numerical Results (–3), Angle Mode (–17, –18), Infinite Result Exception (–22)

Input/Output:

Level 1/Argument 1Level 1/Item 1

 

 

z

→

tan z

 

 

'symb'

→

'TAN(symb)'

 

 

x_unitangular

→

tan (x_unitangular)

 

ATAN, COS,

 

 

 

See also:

SIN

 

 

TAN2CS2

 

 

 

 

Type:

Command

 

 

Description:

Replaces tan(x) terms in an expression with (1-cos(2x))/sin(2x) terms.

 

Access:

Catalog, …µ

 

 

Input:

An expression

 

 

Output:

The transformed expression.

 

 

Flags:

Exact mode must be set (flag –105 clear).

 

 

 

Numeric mode must not be set (flag –3 clear).

 

 

 

Radians mode must be set (flag –17 set).

 

 

Example:

Replace tan(x) terms in the function:

 

 

 

( tan (x))2

 

 

Command:

TAN2CS2(TAN(X)^2)

 

 

Result:

((1-COS(2*X))/SIN(2*X))^2

 

 

See also:

TAN2SC, TAN2SC2

 

 

 

 

 

 

 

TAN2SC

 

 

 

 

Type:

Command

 

 

Description:

Replaces tan(x) sub-expressions with sin(x)/cos(x).

 

 

Access:

PTRIG, Trigonometry, …ÑL

 

 

3-248 Full Command and Function Reference