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⋅

 

(1 + i ⋅ x)

 

 

L------------------------

 

 

 

 

 

 

 

 

 

1 + x2

ASINH(x)

 

–L( 1 + x2 – x)

ACOSH(x)

 

π

 

 

 

 

 

 

2

 

2

 

 

–--2+ i ⋅ L(

1 – x

 

+ i ⋅ x)

ATANH(x)

 

 

 

(1 – x)

 

 

 

 

–L------------------

 

 

 

 

 

 

 

 

 

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)

 

SIH(x) ⋅ COSH(y) + COSH( x) ⋅ SIH( x)

COSH(x + y)

 

COSH(x) ⋅ COSH(y) + SIH( x) ⋅ SIH( y)

TANH(x + y)

 

TAH(x) + TAH( y)

 

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

 

 

1 + TAH( x) ⋅

TAH( y)

 

 

 

 

 

 

 

 

 

 

 

 

→TRG Expansions

 

 

 

 

 

 

 

 

Function

 

Expansion

 

 

 

 

 

 

 

 

 

 

 

EXP (x)

 

COS

x

+ SI

x

⋅ i

 

 

--i

 

--

 

 

 

 

 

 

 

i

 

E-4 Technical Reference