HP 40gs User Manual page 222

hp40g+.book Page 40 Friday, December 9, 2005 1:03 AM
HALFTAN
SINCOS
TAN2CS2
14-40
Typing:
ATAN2S(ATAN(X))
gives:
⎛ ⎞
x
⎜ ------------------ ⎟
asin
⎝ ⎠
2
x + 1
Transform in terms of tan(x/2)
HALFTAN has a trigonometric expression as an
argument.
HALFTAN transforms sin(x), cos(x) and tan(x) in the
expression, rewriting them in terms of tan(x/2).
Typing:
2
HALFTAN(SIN(X)
2
gives (SQ(X) = X ):
2
x
⎛ ⎞
⎛ ⎞
⋅
-- -
2 tan
⎝ ⎠
⎜ ⎟
2
---------------------------------------
⎜ ⎟
+
⎜ x ⎟
⎛ ⎛ ⎞ ⎞
-- -
SQ tan + 1
⎝ ⎠
⎝ ⎝ ⎠ ⎠
2
or, after simplification:
1
Transform the complex exponentials into sin and cos
SINCOS takes an expression containing complex
exponentials as an argument.
SINCOS then rewrites this expression in terms of sin(x)
and cos(x).
Typing:
SINCOS(EXP(i · X))
gives after turning on complex mode, if necessary:
cos(x) + i · sin(x)
Transform tan(x) with sin(2x) and cos(2x)
TAN2CS2 has a trigonometric expression as an
argument.
2
+ COS(X) )
2
x
⎛ ⎛ ⎞ ⎞
⎛ ⎞
-- -
1 SQ – tan
⎝ ⎝ ⎠ ⎠
⎜ ⎟
2
---------------------------------------
⎜ ⎟
⎜ x ⎟
⎛ ⎛ ⎞ ⎞
-- -
SQ tan + 1
⎝ ⎠
⎝ ⎝ ⎠ ⎠
2
Computer Algebra System (CAS)