And with x=0, using the x-axis with degrees, (i.e. to 360 e.t.c) the gradient at x=0, is , even check using the calculator. If you were to convert that back into radians then it would be 1, as expected.
Again, you are mistaken. There is no such thing as gradient in radians or degrees -- gradient has nothing to do with angles!
If you had a right angled triangle, with lengths 1, 1 and sqrt(2).
The angle of the slope is, you could say, 45 degrees. What is the gradient? The gradient is rise/run = 1. It is not 180/pi or whatever you claim it to be.
That is true, I think I know what is going wrong here. When you change the mode on the calculator, it changes the scaling of the graphs and the way the derivatives come out. Thats why the it says the gradient is pi/180=0.02 instead of 1. Effectively what the calculator is doing is evaluating the derivative and converting it back. The gradient thing is wrong. But what I'm trying to get at is that if you put the calculator in degrees mode, then it will give you a derivative with the extra junk in it.
So in short, put it in radian mode and convert everything to radians. It won't fail you and it won't confuse the hell out of you.
Sorry about all this mess above.
Yeah, the calculator does a lot of things 'behind the scenes' haha. Of course, every problem is solved as long as you use radians, as you said.
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