How to solve equation with arctan in Wolfram|Alpha?

Questions
,
1

I’m using the following calculation to find the degree of camber using some measurements:

arctan((AD-BC)/AB)

Using this calculation I get:
arctan((32.9-25.4)/381) = 1.128 degrees

My variable is in this exercise is 32.9 so we’ll call that X - and I want my degrees to equal 2.4. What should X be to equal approximately 2.4 degrees?

E.g. arctan((x-25.4)/381) = 2.4

I can’t for the life of me figure out how to get Wolfram|Alpha to solve an approximation for this!! Any help would be appreciated. Note: I don’t require it to be EXACTLY 2.4, just close!

2

I assume all your measurements and your x are real numbers.

If I can’t get Wolfram|Alpha to find when arctan((x-25.4)/381) equals 2.4 I try a plot

plot arctan((x-25.4)/381), x= -10^4 to 10^4

or

LinkToWA

and that shows me that your arctan ranges from -pi/2 to pi/2 and that is why it isn’t finding a solution when you ask it where that equals 2.4

3

Thanks,

Yes, those are all measurements in millimeters. In the meantime I simply guessed numbers and the closest result to 2.4 degrees is about 1 5/8" or ~41.3mm. I’d love to know how to find it mathematically, however!

Thank you for your time.

4

What do you think about this?

angle = ArcTan[a (x - b)]
equation = y == Tan[angle]
Solve[equation, x]

Tan[ArcTan[(x - 25.4)/381]] == Tan[2.4]
5

You probably asking for a solution like this:

NSolve[ArcTan[(x - 25.4), 381] == 2.4, x]

This takes the quadrant into account - refer to the documentation on ArcTan.