hp40g+.book Page 40 Friday, December 9, 2005 1:03 AM

 

Typing:

 

 

 

 

 

 

 

 

 

 

 

ATAN2S(ATAN(X))

 

 

 

 

 

 

 

gives:

 

 

 

 

 

 

 

 

 

 

 

 

⎛

x

 

⎞

 

 

 

 

 

 

 

 

asin⎜------------------⎟

 

 

 

 

 

 

 

 

 

⎝

x2 + 1⎠

 

 

 

 

 

 

 

HALFTAN

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:

 

 

 

 

 

 

 

 

 

 

 

HALFTAN(SIN(X)2 + COS(X)2)

 

gives (SQ(X) = X2):

 

 

 

 

 

 

 

⎛

2

⋅ tan

⎛ x⎞

⎞ 2

⎛

1 – SQ

⎛

tan

⎛ x⎞⎞ ⎞ 2

 

⎜

--

⎟

⎜

⎝

 

--

 

 

 

 

⎝2⎠

 

 

⎝2⎠⎠ ⎟

 

⎜

---------------------------------------⎟ +

⎜

---------------------------------------⎟

 

⎜

⎛

⎛ x⎞⎞

⎟

⎜

⎛

⎛ x⎞⎞

⎟

 

⎝SQ⎝ tan⎝

--⎠⎠

+ 1⎠

⎝SQ⎝ tan⎝--⎠⎠

+ 1⎠

 

 

 

 

2

 

 

 

 

2

 

 

 

or, after simplification:

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

SINCOS

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)

 

 

 

 

 

 

TAN2CS2

Transform tan(x) with sin(2x) and cos(2x)

 

TAN2CS2 has a trigonometric expression as an

 

argument.

 

 

 

 

 

 

 

 

 

14-40

 

 

Computer Algebra System (CAS)