Min and max slope? Max angle we can rotate graph?

f(x) = e⁴ˢᶦⁿ⁽ˣ⁾ - 3x

What is the maximum angles we can rotate this about the origin and still have a proper function?

My work

f'(x) = e⁴ˢᶦⁿ⁽ˣ⁾*4cos(x) - 3

f''(x) = [ e⁴ˢᶦⁿ⁽ˣ⁾*4cos(x)*4cos(x) ] - [ 4e⁴ˢᶦⁿ⁽ˣ⁾*sin(x) ] = 0

From symbolab online calculator, solving for x in the interval [-2pi, 2pi]

x = 1.08175 + 2pi, and pi - 1.08175 + 2pi

Plugging these into f'(x),

The maximum slope = 61.19

The minimum slope = -67.19

My questions

Q1) What is the maximum acute angle through which the graph can be rotated counter-clockwise? Why is it 90 - arctan (61.19) = 0.936?

Q2) What is the maximum acute angel through which the graph can be rotated clockwise? Why is it 90 - arctan (-67.19579) = 179.147?TL;DR, Why do we calculate 90 - arctan for rotating the graph? I have no idea what rotating a graph even means...