Trig simplifying hp50g
04-21-2015, 08:37 AM
Post: #1
 attle123 Junior Member Posts: 1 Joined: Apr 2015
Trig simplifying hp50g
hello,

when i was playing around with the hp50g, i was having a hard time of simplifying trig equations with tan() and sin() inside a single equation. E.g: if i wished to simplify (sin(x)^2)/cos(x), the answer would be sin(x)*tan(x). however i simply could not get the calculator to give this answer. Anyone able to give me a hand?

Thanks
04-21-2015, 12:32 PM (This post was last modified: 04-21-2015 12:37 PM by Thomas Ritschel.)
Post: #2
 Thomas Ritschel Member Posts: 66 Joined: Feb 2014
RE: Trig simplifying hp50g
There are quite a few commands for manipulating trigonometric functions hidden in the Catalog (CAT = right-shift SYMB), for example the TRIGSIN and TRIGTAN commands.

If you have SIN(X)/COS(X) on the stack, TRIGTAN will yield TAN(X) as expected.

However, for your example TRIGTAN (followed by EVAL) will produce TAN(X)^2 * COS(X), which is also correct, but not what you want. Setting flag 116 ("Prefer sin(x)") doesn't help.

Maybe someone else has a solution...

BTW, on the HP Prime the following works: simplify(cos2sintan(SIN(x)^2/COS(x))) = SIN(x) * TAN(x)
04-22-2015, 11:16 AM (This post was last modified: 04-22-2015 11:28 AM by Gilles.)
Post: #3
 Gilles Member Posts: 171 Joined: Oct 2014
RE: Trig simplifying hp50g
(04-21-2015 12:32 PM)Thomas Ritschel Wrote:  There are quite a few commands for manipulating trigonometric functions hidden in the Catalog (CAT = right-shift SYMB), for example the TRIGSIN and TRIGTAN commands.

You can access more easily to these functions with "LShift TRIG"

To rewrite algebraic expression RShift CONVERT REWRITE is also interesting

All these functions can be used in EQW and can be applied to a subset of the equation. It's easy (POWEXPAND) to change :

SIN(X)²
------
COS(X)

in

SIN(X).SIN(X)
-------------
COS(X)

but I don't know how to change this in
Code:
         SIN(X) SIN(X).-------         COS(X)
Perhaps you can write a small program with the MATCH command.
04-22-2015, 12:34 PM
Post: #4
 Tugdual Senior Member Posts: 764 Joined: Dec 2013
RE: Trig simplifying hp50g
To me
$$\sin { (x)*\tan { (x) } }$$ is not a simplified version of $$\frac { { \sin { \left( x \right) } }^{ 2 } }{ \cos { \left( x \right) } }$$ it is just another way to write it.

Not sure what the "simplify" functions of 50g and Prime are trying to do but the 50g answer with flag 116 being set to "Prefer cos" $$\frac { 1-{ \cos { \left( x \right) } }^{ 2 } }{ \cos { \left( x \right) } }$$ which presents a certain interest especially since you can now envisage substitution.

Now in order to find a "tan", I would rather use the TRIGT rewriting command that unfortunately returns a pretty silly and ugly result until you press EVAL as mentioned by Thomas earlier. Note that simplifying $$\tan { \left( x \right) *\sin { \left( x \right) } }$$ quite rapidly becomes tedious and mental and you never get any close to the first form. 50g CAS doesn't happen very capable.
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