Reference Guide

E-4 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)
E
X
P
x
i
×
(
)
E
X
P
x
i
×
(
)
–
(
)
–
2 i×
---------------------------------------------------------------------
COS (x)
E
X
P
x
i
×
(
)
E
X
P
x
i
×
(
)
–
(
)
+
2 i×
---------------------------------------------------------------------
TAN (x)
E
X
P
x
i
2
×
×
(
)
1
–
EXP x i 2××( ) 1+( ) i×
-----------------------------------------------------------
SINH(x)
S
I

x
i
×
(
)
i
×
(
)
–
COSH(x)
C
O
S
x
i
×
(
)
TANH(x)
T
A

x
i
×
(
)
i
–
×
ASIN(x)
i L 1 x
2
– i x×+( )×–
ACOS(x)
π
2
---
i L 1 x
2
– i x×+( )×+
ATAN(x)
i L
1 i x×+( )
1 x
2
+
------------------------
 
 


×–
ASINH(x)
L 1 x
2
+ x –( )–
ACOSH(x)
π
2
---
i L 1 x
2
– i x ×+( )×+
 
 
2
–
ATANH(x)
L
1 x–( )
1 x
2
–
------------------
 
 
 
–
TRG
*
Expansions
Function Expansion
SIN (x + y)
S
I

x
(
)
C
O
S
y
(
)
×
C
O
S
x
(
)
S
I

x
(
)
×
+
COS (x + y)
C
O
S
x
(
)
C
O
S
y
(
)
×
S
I

x
(
)
S
I

y
(
)
×
+
TAN (x + y)
T
A

x
(
)
T
A

y
(
)
+
1 TA x( ) TA y( )×–
------------------------------------------------------
SINH(x + y)
S
I

H
x
(
)
C
O
S
H
y
(
)
×
C
O
S
H
x
(
)
S
I

H
x
(
)
×
+
COSH(x + y)
C
O
S
H
x
(
)
C
O
S
H
y
(
)
×
S
I

H
x
(
)
S
I

H
y
(
)
×
+
TANH(x + y)
T
A

H
x
(
)
T
A

H
y
(
)
+
1 TAH x( ) TA H y( )×+
----------------------------------------------------------------
→TRG Expansions
Function Expansion
EXP (x)
C OS
x
i
--
 
 
SI
x
i
--
 
 
i×+