TI-BASIC:Degree Mode - Revision history

Maintenance script: Automated internal link correction

2016-02-24T23:53:48Z

Automated internal link correction

← Older revision		Revision as of 23:53, 24 February 2016
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	The input is differently interpreted:		The input is differently interpreted:
	* [[TI-BASIC:~~P►Rx(~~\|P►Rx(]], [[TI-BASIC:P►Ry(\|P►Ry(]]		* [[TI-BASIC:P_Rx\|P►Rx(]], [[TI-BASIC:P►Ry(\|P►Ry(]]
	* [[TI-BASIC:Sin\|Sin(]], [[TI-BASIC:Cos\|Cos(]], [[TI-BASIC:Tan\|Tan(]]		* [[TI-BASIC:Sin\|Sin(]], [[TI-BASIC:Cos\|Cos(]], [[TI-BASIC:Tan\|Tan(]]

Maintenance script: Automated superscript correction

2016-02-24T22:23:11Z

Automated superscript correction

← Older revision		Revision as of 22:23, 24 February 2016
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	* [[TI-BASIC:Arcsin\|sin‾¹(]], [[TI-BASIC:Arccos\|cos‾¹(]], [[TI-BASIC:Arctan\|tan‾¹(]]		* [[TI-BASIC:Arcsin\|sin‾¹(]], [[TI-BASIC:Arccos\|cos‾¹(]], [[TI-BASIC:Arctan\|tan‾¹(]]
	* [[TI-BASIC:Polar_Display\|►Polar]] (and complex numbers when in [[TI-BASIC:Re_Thetai\|re^θi]] mode)		* [[TI-BASIC:Polar_Display\|►Polar]] (and complex numbers when in [[TI-BASIC:Re_Thetai\|re^θi]] mode)
	* ^^[[TI-BASIC:Radian_Symbol\|r]]^^, [[TI-BASIC:Degree_Symbol\|°]]		* <sup>[[TI-BASIC:Radian_Symbol\|r]]</sup>, [[TI-BASIC:Degree_Symbol\|°]]

	However, some commands are notably unaffected by angle mode, even though they involve angles, and this may cause confusion. This happens with the [[TI-BASIC:Sinreg\|SinReg]] command, which assumes that the calculator is in Radian mode even when it's not. As a result, the regression model it generates will graph incorrectly in Degree mode.		However, some commands are notably unaffected by angle mode, even though they involve angles, and this may cause confusion. This happens with the [[TI-BASIC:Sinreg\|SinReg]] command, which assumes that the calculator is in Radian mode even when it's not. As a result, the regression model it generates will graph incorrectly in Degree mode.
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	* [[TI-BASIC:Radian_Mode\|Radian]]		* [[TI-BASIC:Radian_Mode\|Radian]]
	* ^^[[TI-BASIC:Radian_Symbol\|r]]^^		* <sup>[[TI-BASIC:Radian_Symbol\|r]]</sup>
	* [[TI-BASIC:Degree_Symbol\|°]][[Category:TI-BASIC]]		* [[TI-BASIC:Degree_Symbol\|°]][[Category:TI-BASIC]]
	[[Category:TIBD]]		[[Category:TIBD]]

Maintenance script: Initial automated import

2016-02-24T18:09:53Z

Initial automated import

New page

{{Template:TI-BASIC:Command
|picture=DEGREE.GIF
|summary=Puts the calculator in Degree mode.
|syntax=Degree
|location=While editing a program, press:
# MODE to access the mode menu.
# Use arrows and ENTER to select Degree.
|compatibility=TI-83/84/+/SE
|size=1 byte
}}

The Degree command puts the calculator into Degree mode, where the inputs and/or outputs to trig functions are assumed to be degree angles.

Angles measured in degrees range from 0 to 360, with 0 being an empty angle, 90 being a right angle, 180 being a straight angle, and 360 being a full angle all the way around a circle.

To convert from a degree angle to a radian angle, multiply by 180/π. To go the other way, and get a radian angle from a degree angle, multiply by π/180.

The following commands are affected by whether the calculator is in [[TI-BASIC:Radian_Mode|Radian]] or Degree mode:

The input is differently interpreted:
* [[TI-BASIC:P►Rx(|P►Rx(]], [[TI-BASIC:P►Ry(|P►Ry(]]
* [[TI-BASIC:Sin|Sin(]], [[TI-BASIC:Cos|Cos(]], [[TI-BASIC:Tan|Tan(]]

The output is differently expressed:
* [[TI-BASIC:Angle|Angle(]]
* [[TI-BASIC:R_Ptheta|R►Pθ(]]
* [[TI-BASIC:Arcsin|sin‾¹(]], [[TI-BASIC:Arccos|cos‾¹(]], [[TI-BASIC:Arctan|tan‾¹(]]
* [[TI-BASIC:Polar_Display|►Polar]] (and complex numbers when in [[TI-BASIC:Re_Thetai|re^θi]] mode)
* ^^[[TI-BASIC:Radian_Symbol|r]]^^, [[TI-BASIC:Degree_Symbol|°]]

However, some commands are notably unaffected by angle mode, even though they involve angles, and this may cause confusion. This happens with the [[TI-BASIC:Sinreg|SinReg]] command, which assumes that the calculator is in Radian mode even when it's not. As a result, the regression model it generates will graph incorrectly in Degree mode.

Also, complex numbers in polar form are an endless source of confusion. The angle( command, as well as the polar display format, are affected by angle mode. However, complex exponentials (see the [[TI-BASIC:E_Exponent|e^(]] command), defined as <math>e^{i\theta}=\cos\theta+i\sin\theta</math>, are evaluated as though in Radian mode, regardless of the angle mode. This gives mysterious results like the following:

Degree:re^θi
Done
e^(πi)
1e^(180i)
Ans=e^(180i)
0 (false)

Overall, it's better to put your calculator in Radian mode when dealing with polar form of complex numbers, especially since no mathematician would ever use degrees for the purpose anyway.

= Optimization =

It's sometimes beneficial to use the [[TI-BASIC:Degree_Symbol|°]] symbol instead of switching to Degree mode. The ° symbol will make sure a number is interpreted as a degree angle, even in radian mode, so that, for example:

Radian
Done
sin(90)
-.8011526357
sin(90°)
1

This is smaller when only one trig calculation needs to be done. Also, it doesn't change the user's settings, which are good to preserve whenever possible.

= Related Commands =

* [[TI-BASIC:Radian_Mode|Radian]]
* ^^[[TI-BASIC:Radian_Symbol|r]]^^
* [[TI-BASIC:Degree_Symbol|°]][[Category:TI-BASIC]]
[[Category:TIBD]]