Regarding units of output value

Questions
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1

Hi All,
I am using the following command, to find maximum of a function:

FindMaximum[Cos[phi Degree] (1 - 0.4 Sin[5 Degree + phi Degree]^2), phi]

And getting the following Out put:

{0.998309, {phi -> -2.22083}}

I know Mathematica by default use the values of an angle in Radians, therefore, I used the Degree with angles in INPUT.

Now, I am not sure about the value of output given in Mathematica. Whether its’ phi=-2.22083 Degree OR -2.22083 Radians?

2

Regarding units of output value

3

I’d expect the output to be in radians. All the Degree multiplier does is convert the specified value form degrees to radians. Try typing Degree//N to get its numeric value. If you want to retain the units in the output, you could try wrapping the angular variables, x, in Quantity[x,”AngularDegrees”] - tip, you can generate a nicely formatted version of this Quantity expression by typing ctrl= followed by “x Angular Degrees”. This might return a Quantity result (in this case either radians or angular degrees). I’m not sure whether it would have the desired outcome, but might be worth a go to see what you get.

4

Thanks for the reply.
Can you elaborate :
"you could try wrapping the angular variables, x, in Quantity[x,”AngularDegrees”] "

Do you mean I use the command
FindMaximum[Cos[phi] (1 - 0.4 Sin[5 Degree + phi]^2), phi “AngularDegrees”]

5

Sorry, haven’t been near my computer for a while. Having checked, I don’t think my suggestion works, I wasn’t sure that it would - see attached notebook. But the value of phi in your output is definitely in radians.

Units.nb (18.6 KB)

6

The result is in terms of degrees. Plot the input expression with phi ranging from -90 to 90 and you will see this.

7

Yes, you’re quite right. My mistake.

8

Yes, you’re quite right. My mistake.

9

Regarding units of output value

10

Thank you for this very nice demonstration.
I realised that, in my original function, some of the quantities are in Radians and some are in Degree. Therefore, my results were not consistent.

Thanks for your time.