Getting a 35S/33S to behave

[Matt Agajanian]

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?

[r. pienne]

Try it and see.

[Matt Agajanian]

Okie doke.

[Thomas Klemm]

(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

[Matt Agajanian]

(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.

[Matt Agajanian]

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?

[Thomas Klemm]

(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