The ° symbol used after an angle makes sure the angle is interpreted as being in degrees. If the calculator is already in degree mode, x° is equal to x; in radian mode, x° is equal to π*x/180; and in gradian mode, x° is equal to 10*x/9.
If you're using degree measure extensively in a program, it's a better idea to use setMode() to switch to degree mode and not worry about this. However, there are two reasons you might want to use °:
- If you need an angle in degrees only once or twice, don't bother changing the mode setting.
- In a function, you're forced to use °, since setMode() isn't valid in a function.
In radian mode:
:sin(30) sin(30) :sin(30°) 1/2 :180° π
In degree mode (no conversion is necessary, so no conversion is done):
:sin(30) 1/2 :sin(30°) 1/2 :180° 180
Another possible use of ° is to write an angle in degrees, minutes, and seconds as x°y'z" (using the usual apostrophe and quote symbols) — this stands for x degrees, y minutes (equal to 1/60th of a degree) and z seconds (equal to 1/60th of a minute). There's no "degree/minute/second" mode setting, so an angle entered in this form will always be simplified: first to (x+y/60+z/3600)2 degrees, and then (if necessary) converted to the correct angle measure. However, you can use ▶DMS to express output in this form.