SOLVED Hp Prime - CAS inconsistent derivatives of sin, cos, tan
05-29-2014, 10:28 AM (This post was last modified: 05-29-2014 01:19 PM by CR Haeger.)
Post: #1
 CR Haeger Member Posts: 275 Joined: Dec 2013
SOLVED Hp Prime - CAS inconsistent derivatives of sin, cos, tan
In CAS I notice now that taking first derivative of sin, cos or tan yields different results if in radians versus degrees mode.

In radians mode, d sin(x)/dx gives cos(x)
In degrees mode it gives PI * cos(x)/180

I assume these should be consistent and match the result from radians mode?

Running 6030 firmware.
05-29-2014, 10:40 AM
Post: #2
 cdecastro Junior Member Posts: 22 Joined: Dec 2013
RE: Hp Prime - CAS inconsistent derivatives of sin, cos, tan
This is correct. The derivative rules d(sin(x))=cos(x) etc.. only hold when the angle is measured in radians. If the angle is in degrees the appropriate rule is found by applying the chain rule.

i.e. if the given angle x is measured in radians as x_rad and in degrees as x_deg, then x_deg = 180/Pi * x_rad, so

d( sin( Pi/180 * x_deg ) ) = cos( Pi/180 * x_deg ) * Pi/180 (using chain rule)
= cos( Pi/180 * x_deg) * Pi/180

Regards,
Chris
05-29-2014, 01:20 PM (This post was last modified: 05-29-2014 01:22 PM by Tugdual.)
Post: #3
 Tugdual Senior Member Posts: 756 Joined: Dec 2013
RE: Hp Prime - CAS inconsistent derivatives of sin, cos, tan
(05-29-2014 10:40 AM)cdecastro Wrote:  This is correct. The derivative rules d(sin(x))=cos(x) etc.. only hold when the angle is measured in radians. If the angle is in degrees the appropriate rule is found by applying the chain rule.

i.e. if the given angle x is measured in radians as x_rad and in degrees as x_deg, then x_deg = 180/Pi * x_rad, so

d( sin( Pi/180 * x_deg ) ) = cos( Pi/180 * x_deg ) * Pi/180 (using chain rule)
= cos( Pi/180 * x_deg) * Pi/180

Regards,
Chris
Correct
$$(g\circ f)'=g'\circ f*f'\\ \sin { (a*x)'=cos(a*x)*a }$$
While converting from degree to radian you get the conversion factor
$$a=\frac { \pi }{ 180 }$$
05-29-2014, 01:22 PM (This post was last modified: 05-29-2014 01:26 PM by CR Haeger.)
Post: #4
 CR Haeger Member Posts: 275 Joined: Dec 2013
RE: SOLVED Hp Prime - CAS inconsistent derivatives of sin, cos, tan
Yes, of course you and the Prime are both correct...

I got tripped up as I used to do DERVX in CAS with the 50G and it forced me to switch from deg --> rad. The Prime provides correct answers in either mode. This would seem to be a great feature for Geometry teachers.

Thanks again.

ps TW: 3, Me: 0
05-29-2014, 01:30 PM
Post: #5
 Tim Wessman Senior Member Posts: 2,277 Joined: Dec 2013
RE: SOLVED Hp Prime - CAS inconsistent derivatives of sin, cos, tan
I would think it is more 3 to <some much larger number> and not 0...

TW

Although I work for the HP calculator group, the views and opinions I post here are my own.
05-29-2014, 01:53 PM
Post: #6
 CR Haeger Member Posts: 275 Joined: Dec 2013
RE: SOLVED Hp Prime - CAS inconsistent derivatives of sin, cos, tan
(05-29-2014 01:30 PM)Tim Wessman Wrote:  I would think it is more 3 to <some much larger number> and not 0...

Nope - 3-0 (since the new firmware release). However, Im still waiting to hear if there is a way to recover my custom spreadsheet apps content following the upgrade. Id prefer not to retype all this back in.
05-29-2014, 02:11 PM
Post: #7
 Michael de Estrada Senior Member Posts: 361 Joined: Dec 2013
RE: SOLVED Hp Prime - CAS inconsistent derivatives of sin, cos, tan
(05-29-2014 01:53 PM)CR Haeger Wrote:
(05-29-2014 01:30 PM)Tim Wessman Wrote:  I would think it is more 3 to <some much larger number> and not 0...

However, I'm still waiting to hear if there is a way to recover my custom spreadsheet apps content following the upgrade. Id prefer not to retype all this back in.

Start typing.
05-31-2014, 01:29 AM
Post: #8
 rprosperi Senior Member Posts: 5,066 Joined: Dec 2013
RE: SOLVED Hp Prime - CAS inconsistent derivatives of sin, cos, tan
(05-29-2014 01:53 PM)CR Haeger Wrote:  ...Id prefer not to retype all this back in.

(05-29-2014 02:11 PM)Michael de Estrada Wrote:  Start typing.

Yup! What he said... It got me too.

--Bob Prosperi
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