HP50g - CAS simple question (sin^2 + cos^2)

[andy11]

My 50g does not give 1 in answer to the sin(x)^2+cos(x)^2, it just repeats sin(x)^2+cos(x)^2.

Am I doing something wrong?

My TI nspire and Casio classpad both give 1 in that case.

I bought 50g as a second hand, made a cold reset (ON/F1/F6) but it still  does not give 1.

For (x^2 - 1)/(x-1) HP50g gives correct (x+1).

[pin224466]

with the following on level 1 of the stack (in RPN mode)

'(SIN(X)^2)+(COS(X)^2)'

execute the following function:

SIMPLIFY

result

1

[pin224466]

here's a repeat from a couple of my prior posts:

in general.... don't forget the flags, they can affect how formulas/equations are simplified/modified...

for example flag -111, -113, -114, -122 ... -1, -2, -3.

here are some important equation manipulation functions:

EVAL, DISTRIB, FDISTRIB, COLLECT, EXPAND, FACTOR, COLCT, SIMPLIFY

and then there are the exponential/trig equation manipulation functions:

acos2s

asin2c

asin2t

atan2s

sincos

exp2hyp

exp2pow

expln

lncollect

texpand

tcollect

tlin

trigsin

trigcos

trigtan

trig

tan2cs2

tan2sc

tan2sc2

halftan

finally, there is the most flexible equation manipulation function... this one allows the 50G user to define how to change the equation on the stack:

SUBST

↓MATCH

↑MATCH

you can get a copy of the Advanced Users Reference manual (and all other manuals) that details the above flags and commands from here:

http://h20000.www2.hp.com/bizsupport/TechSupport/DocumentIndex.jsp?contentType=SupportManual&lang=en...

[HP-MACH]

Hi!, andy11:

See, your example ...

 now, press ...

The result is ...

[andy11]

Thank you all

I found by chance even simpler solution:

With an expression on the 1st level of stack, press  "down" key, then soft key EDIT ant finally soft key SIMP

[pin224466]

that is correct,  down arrow (with an equation on the stack) enters the editor.

you should not need to press EDIT

the SIMP softkey is actually executing SIMPLIFY

you will find that in editor, you can select (highlight) specific portions of an equation and EVAL or SIMPLIFY them

while in the editor, if you press NXT, you will see the softkey CMDS   or select the CAT.  With the equation highlighted (or piece of the equation highlighted), pick the command you want to execute, then select the EVAL softkey.  Note that sometimes, depending on the function selected, EVAL may not be required.

At this point, if you press ENTER, the result will be returned to the stack.

However, if you press ON/Cancel, the original equation will be returned to the stack.

With complex equations, you can highlight just a portion of the equation, and using the above method, perform a function on only the highlighted piece of the equation.

for example, with your original equation on level 1 of the stack (in RPN mode)...

'(SIN(X)^2)+(COS(X)^2)'

DOWN ARROW

then

DOWN ARROW

DOWN ARROW

only the SIN(X) is highlighted (and not the exponent).

now execute CAT (right shift CAT)

-select the TRIGTAN  function and then press F6 (OK)

-to see the changes just made to the equation press ENTER

-press UP ARROW

-select F2 (VIEW)

(the cos(x) function was not changed by TRIGTAN, only the sin(x) function was affected)

.......

[HP-MACH]

Hi!, andy11:

The function SIMPLIFY, work with EVAL.

Look this, in SysRPL ...

::

 xEVAL>

 ::

  xNOEVAL

  SYMBOL

     ID X

     xSIN

     Z2_

     x^

     ID X

     xCOS

     Z2_

     x^

     x+

   ;

   SYMBOL

       xSIMPLIFY

   ;

   BINT1

   xCMDAPPLY

 ;

;

@

Store it, with any name, p.e. 'EQ'

and press STO

Now, press the function key (F1...F6) just down, to EQ.

You result is ... 1

[andy11]

Thank you Miguel and pin, all your hints are very useful

Sorry for more questions. All 1 to 4 below are standard algebraic expressions

1. cosh(x)^2 - sinh(x)^2     = 1
2. sinh(x) + cosh(x)               = exp(x)
3. cos(x) +i*sin(x)                 = exp(i*x)
4. (exp(x) - exp(-x))/2         = sinh(x)

 50g after SIMPLIFY gives correct answer to 1 & 2, the 3 & 4 are not resolved 

"i" in 3-rd expression is imaginary unit (i^2 = -1).

The 103 flag (complex on) is set, the112 (i simplified) seems to have no influence.

TI nspire  can resolve all 4 expressions.

Thank you for your time

[pin224466]

calculator set to EXACT

COMPLEX mode on

flag -3 clear

3. cos(x) +i*sin(x)

EXPLN

EVAL

result

e^iX

4. (exp(x) - exp(-x))/2

EXP2HYP

result

SINH(X)

[HP-MACH]

Hi!, andy11:

3) Use EXPLN function ... Transforms the trigonometric terms, in an expression to exponential and logarithmic terms.

Configure FLAGS ...

Exact mode must be set (flag –105 clear).

Numeric mode must not be set (flag –3 clear).

Radians mode must be set (flag –17 set).

Complex mode must be set (flag –103 set).

 

4) Use EXP2HYP function ... Converts expressions involving the exponential function, into expressions with hyperbolic functions.

Configure FLAGS ...

Exact mode must be set (flag –105 clear).

Numeric mode must not be set (flag –3 clear).