Calculate the angle of inclination?
This function is given:
f(x) = -0.2x^2 – 3x +1.2
Normally I calculate an angle by first solving X with
solve(0 = -0.2x^2 – 3x + 1.2 , x)
This results in X, which I then enter into my calculator as the X-value for the first derivative. This then produces a number, which I enter into arctan() to obtain the angle.
So:
- solve(0 = function) x = 123
- d/dx(function)|x = 123
- arctan(result 2) = angle
But how exactly do I do it with the angle of inclination?
My solution would be (I don't know if it's right!)
- Step: 1. Derivation
- Step: solve for X value = -7.5
- Step: arctan(-7.5) = 82.4 degrees
Is that true?
(1 votes)
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f(x) = -0.2×2 – 3x + 1.2
f'(x) = -0.4x – 3
A pitch angle results, for example, from the slope of a function rod end at the point (x,f(x)). If, for example, the positive zero of f(x): x1 ~ 0.389867, then the gradient of the tangent at this zero f'(x1) ~-3.1559
The pitch angle of the tangent is then arctan(-3.1559). The corresponding value in degree depends on the direction of rotation and on which axis one refers to 0 degrees.
The angle in the mathematical sense is pi + arctan(-3.1559) ~ 107.58°
Thanks for the star