Post Reply 
Getting a 35S/33S to behave
04-24-2014, 06:02 PM (This post was last modified: 04-24-2014 06:05 PM by Matt Agajanian.)
Post: #1
Getting a 35S/33S to behave
Hello all.

Let me cite the trig issue of the 33s/35s. Although trig operations near 90 degrees are a dud, is there a means to normalise a near 90 value so that a trig function can return an accurate result? Would converting the angle from degrees to radians/grads and calculating the trig function in radians/grads help?
Find all posts by this user
Quote this message in a reply
04-24-2014, 06:08 PM
Post: #2
RE: Getting a 35S/33S to behave
Try it and see.
Find all posts by this user
Quote this message in a reply
04-24-2014, 06:15 PM
Post: #3
RE: Getting a 35S/33S to behave
Okie doke.
Find all posts by this user
Quote this message in a reply
04-24-2014, 07:30 PM
Post: #4
RE: Getting a 35S/33S to behave
(04-24-2014 06:02 PM)Matt Agajanian Wrote:  Although trig operations near 90 degrees are a dud, is there a means to normalise a near 90 value so that a trig function can return an accurate result?
Use \(\sin(x)=\cos(90-x)\) and \(\tan(x)=\frac{1}{\tan(90-x)}\).

Quote:Would converting the angle from degrees to radians/grads and calculating the trig function in radians/grads help?
Probably not. Replace \(90\) by \(\frac{\pi}{2}\) in the formulas above when using radians mode.

Cheers
Thomas
Find all posts by this user
Quote this message in a reply
04-24-2014, 07:32 PM
Post: #5
RE: Getting a 35S/33S to behave
(04-24-2014 07:30 PM)Thomas Klemm Wrote:  
(04-24-2014 06:02 PM)Matt Agajanian Wrote:  Although trig operations near 90 degrees are a dud, is there a means to normalise a near 90 value so that a trig function can return an accurate result?
Use \(\sin(x)=\cos(90-x)\) and \(\tan(x)=\frac{1}{\tan(90-x)}\).

Quote:Would converting the angle from degrees to radians/grads and calculating the trig function in radians/grads help?
Probably not. Replace \(90\) by \(\frac{\pi}{2}\) in the formulas above when using radians mode.

Cheers
Thomas

Thanks! Those are normalisation techniques I can live with.
Find all posts by this user
Quote this message in a reply
04-24-2014, 10:05 PM
Post: #6
RE: Getting a 35S/33S to behave
Okay here's a test:

sin(1.566981956radians) and cos(0.003814371radians) yield 0.999992725295 on the 35S

sin(1.5669819576radians) and cos(0.00381437113radians) yields 0.999992725295 on the 11C

sin(1.5669819576radians) and cos(0.00381437113radians) yields 0.999992725303 on the 32S-II

sin(1.5669819576radians) and cos(0.00381437113radians) yields 0.999992725303 on the 42S


So, what's the verdict?
Find all posts by this user
Quote this message in a reply
04-25-2014, 12:54 AM
Post: #7
RE: Getting a 35S/33S to behave
(04-24-2014 10:05 PM)Matt Agajanian Wrote:  Okay here's a test:

sin(1.566981956radians) and cos(0.003814371radians) yield 0.999992725295 on the 35S

sin(1.5669819576radians) and cos(0.00381437113radians) yields 0.999992725295 on the 11C
As the HP-11C can only handle 10 digits I assume there's a typo.
I get sin(1.566981956) = 0.9999927253. I might not get why you use different input for the 35S and the other models.

Quote: sin(1.5669819576radians) and cos(0.00381437113radians) yields 0.999992725303 on the 32S-II

sin(1.5669819576radians) and cos(0.00381437113radians) yields 0.999992725303 on the 42S


So, what's the verdict?

It appears there's a problem with small values as well.
From a previous thread about the HP-33S:
Quote:105 * sin(0.0001)


HP-32SII 9.99999998333
HP-33S 9.99999998300
actual 9.99999998333

You could try another identity: \(\sin(x)=2\sin(\frac{x}{2})\cos(\frac{x}{2})\).
Code:
2
/
1
->R
*
2
*
Don't search too long for ->R on the HP-35S.

Cheers
Thomas
Find all posts by this user
Quote this message in a reply
Post Reply 




User(s) browsing this thread: