# Tan2sc2; Taylor0; Tchebycheff - HP 48gII Advanced User's Reference Manual

Graphing calculator.

## TAN2SC2

Type:
Command
Description:
Replaces tan(x) terms in an expression with sin(2x)/1+cos(2x) terms.
P
Access:
TRIG
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).
I n previous versions of the CAS, if flag –116 was set (Prefer sin()), then TAN2SC2 replaced tan(x)
terms with: 1 – Cos(2x)/Sin(2x). This action is now performed by the TAN2CS2 command.
Example:
Replace tan(x) terms in the function:
tan
x
Command:
TAN2SC2(TAN(X)^2)
Result:
(SIN(2*X)/(1+COS(2*X)))^2
HALFTAN, TAN2CS2, TAN2SC

### TAYLOR0

Type:
Function
Description:
Performs a fourth-order Taylor expansion of an expression at x = 0.
Calculus, !Ö
Access:
Input:
An expression
Output:
The Taylor expansion of the 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:
Obtain the fourth-order Taylor series expansion of cos(x) at x=0.
Command:
TAYLOR0(COS(X))
Result:
1/24*X^4+-1/2*X^2+1
DIVPC, lim, TAYLR, SERIES

### TCHEBYCHEFF

Type:
Function
Description:
Returns the nth Tchebycheff polynomial.
Catalog, ...µ
Access:
Input:
A non-negative integer, n.
Output:
The nth Tchebycheff polynomial.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Example:
Obtain the fourth Tchebycheff polynomial.
Command:
TCHEBYCHEFF(4)
Result:
8*X^4-8*X^2+1
HERMITE, LEGENDRE
, Trigonometry, ...ÑL
2
&
LIMITS
SERIES
, P
L
CALC
Computer Algebra Commands 4-73