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.
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 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
$$a=\frac { \pi }{ 180 } $$
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
I would think it is more 3 to <some much larger number> and not 0...
(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 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.
(05-29-2014 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.