SOLVED Hp Prime  CAS inconsistent derivatives of sin, cos, tan

05292014, 10:28 AM
(This post was last modified: 05292014 01:19 PM by CR Haeger.)
Post: #1




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. 

05292014, 10:40 AM
Post: #2




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 

05292014, 01:20 PM
(This post was last modified: 05292014 01:22 PM by Tugdual.)
Post: #3




RE: Hp Prime  CAS inconsistent derivatives of sin, cos, tan
(05292014 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.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 $$a=\frac { \pi }{ 180 } $$ 

05292014, 01:22 PM
(This post was last modified: 05292014 01:26 PM by CR Haeger.)
Post: #4




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 

05292014, 01:30 PM
Post: #5




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. 

05292014, 01:53 PM
Post: #6




RE: SOLVED Hp Prime  CAS inconsistent derivatives of sin, cos, tan
(05292014 01:30 PM)Tim Wessman Wrote: I would think it is more 3 to <some much larger number> and not 0... Nope  30 (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. 

05292014, 02:11 PM
Post: #7




RE: SOLVED Hp Prime  CAS inconsistent derivatives of sin, cos, tan
(05292014 01:53 PM)CR Haeger Wrote:(05292014 01:30 PM)Tim Wessman Wrote: I would think it is more 3 to <some much larger number> and not 0... Start typing. 

05312014, 01:29 AM
Post: #8




RE: SOLVED Hp Prime  CAS inconsistent derivatives of sin, cos, tan
(05292014 01:53 PM)CR Haeger Wrote: ...Id prefer not to retype all this back in. (05292014 02:11 PM)Michael de Estrada Wrote: Start typing. Yup! What he said... It got me too. Bob Prosperi 

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