Trigonometric Expansions - HP 48gII Advanced User's Reference Manual

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.
SIN (x)
COS (x)
TAN (x)
SINH(x)
COSH(x)
TANH(x)
ASIN(x)
ACOS(x)
ATAN(x)
ASINH(x)
ACOSH(x)
ATANH(x)
SIN (x + y)
COS (x + y)
TAN (x + y)
SINH(x + y)
COSH(x + y)
TANH(x + y)
EXP (x)
E - 4 Technical Reference
"DEF Expansions
Function
TRG * Expansions
Function
SIN H x
COSH x
"TRG Expansions
Function
Expansion
EXP x i – EXP – x
-------------------------------------------------------------------- -
2 i
EXP x i + EXP – x
-------------------------------------------------------------------- -
2 i
EXP x i 2 – 1
---------------------------------------------------------- -
EXP x i 2 + 1
– SIN x i i
COS x i
T A N x i i –
2
– i LN 1 x – + i
2
-- - + i LN 1 – x + i
2
⎛ ⎞
1 + i x
– i LN ⎜ ------------------------ ⎟
⎝ ⎠
2
1 + x
2
– LN 1 + x – x
⎛
2
-- -
– + i LN 1 x – + i
⎝
2
⎛ ⎞
1 x –
– LN ⎜ ----------------- - ⎟
⎝ ⎠
2
1 x –
Expansion
SIN x COS y + COS x
COS x COS y + SIN x
TA N x + TAN y
----------------------------------------------------- -
1 – TAN x TAN y
COS H y + COSH x
COS H y + SINH x
TAN H x + TANH y
--------------------------------------------------------------- -
1 + TANH x TANH y
Expansion
x x
⎛ ⎞ ⎛ ⎞
C OS - - + SIN - -
⎝ ⎠ ⎝ ⎠
i i
i
i
i
x
x
2
⎞
x
⎠
SIN x
SIN y
SINH x
SINH y
i
,
*