HP 50g Graphing, 48gII Graphing manual →DEF Expansions, E4 Technical Reference

Trigonometric Expansions

The following tables list expansions for trigonometric functions in Radians mode when using the →DEF, TRG*, and →TRG operations. These operations appear in the Equation Writer RULES menu.

→DEF Expansions

Function

Expansion

SIN (x)

EXP(x ⋅ i) – EXP(–(x⋅ i))

--------------------------------------------------------------------

2

⋅ i

COS (x)

EXP(x ⋅ i) + EXP(–(x⋅ i))

---------------------------------------------------------------------

2

⋅ i

TAN (x)

EXP(x ⋅ i ⋅ 2) – 1

----------------------------------------------------------

(EXP(x

⋅ i

⋅ 2)

+ 1) ⋅ i

SINH(x)

–(SI( x ⋅ i) ⋅ i)

COSH(x)

COS( x ⋅ i)

TANH(x)

TA

( x ⋅ i) ⋅ –i

ASIN(x)

–i⋅ L ( 1 – x

2

+ i ⋅ x)

ACOS(x)

-- + i ⋅ L

(

1 – x

+ i ⋅ x)

π

2

2

ATAN(x)

–i⋅ L

 (1 + i ⋅ x)

 ------------------------





1 + x2



ASINH(x)

–L

(

1 + x2 – x)

ACOSH(x)

 π

2

 2

–--2+ i ⋅ L

(

1 – x

+ i ⋅ x)

ATANH(x)

–L

 (1 – x) 

 ------------------





1 – x2

TRG* Expansions

Function

Expansion

SIN (x + y)

SI (x) ⋅ COS(y) + COS(x) ⋅ SI

(x)

COS (x + y)

COS(x) ⋅ COS(y) + SI

(x) ⋅ SI

(y)

TAN (x + y)

TA

(x) + TA

( y)

------------------------------------------------------

1 – TA x( ) ⋅

TA y( )

SINH(x + y)

SI H(x) ⋅ COSH(y) + COSH( x) ⋅ SI

H( x)

COSH(x + y)

COSH(x) ⋅ COSH(y) + SI

H( x) ⋅ SI

H( y)

TANH(x + y)

TA H(x) + TA H( y)

---------------------------------------------------------------

1 + TA H x( ) ⋅

TA H y( )

→TRG Expansions

Function

Expansion

EXP (x)

COS

 x

+ SI

 x

⋅ i

 --i

--

 i

E4 Technical Reference