HP 48GII

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
N
x
i×()i×()
–
COSH(x)
C
O
S
x
i×()
TANH(x)
T
A
N
x
i×()i
–
×
ASIN(x)
iLN1 x
2
– ix×+()×–
ACOS(x)
π
2
---
iLN1 x
2
– ix×+()×+
ATAN(x)
iLN
1 ix×+()
1 x
2
+
------------------------
⎝⎠
⎜⎟
⎛
⎞
×–
ASINH(x)
LN 1 x
2
+ x–()–
ACOSH(x)
π
2
---
iLN 1 x
2
– ix×+()×+
⎝⎠
⎛⎞
2
–
ATANH(x)
LN
1 x–()
1 x
2
–
------------------
⎝⎠
⎜⎟
⎛⎞
–
TRG
*
Expansions
Function Expansion
SIN (x + y)
S
I
N
x
()
C
OS y()×
C
OS
x
() S
I
N
x
()×+
COS (x + y)
C
O
S
x
()
C
O
S
y()×
S
I
N
x
()
S
I
N
y()×+
TAN (x + y)
T
A
N
x
()
T
A
N
y()+
1 TAN x() TAN y()×–
------------------------------------------------------
SINH(x + y)
S
I
N
H
x
()
C
OS
H
y
()×
C
OS
H
x
() S
I
N
H
x
()×+
COSH(x + y)
C
OS
H
x
()
C
OS
H
y
()× S
I
N
H
x
() S
I
N
H
y
()×+
TANH(x + y)
TA
N
H
x
() TA
N
H
y()+
1 TANH x() TANH y()×+
----------------------------------------------------------------
"TRG Expansions
Function Expansion
EXP (x)
COS
x
i
--
⎝⎠
⎛
⎞
SIN
x
i
--
⎝⎠
⎛
⎞
i×+