The Degree Command

Command Summary

Puts the calculator in Degree mode.

Command Syntax

Degree

While editing a program, press:

1. MODE to access the mode menu.
2. Use arrows and ENTER to select Degree.

TI-83/84/+/SE

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 radian angle to a degree 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 Radian or Degree mode:

The input is differently interpreted:

The output is differently expressed:

However, some commands are notably unaffected by angle mode, even though they involve angles, and this may cause confusion. This happens with the 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 e^( command), defined as $e^{i\theta}=\cos\theta+i\sin\theta$, 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 ° 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.

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