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Calculus For ML

Calculus For ML

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Pi (π)

It is the circumference / diameter, the ratio of how many diameters it takes to create a circle, always being 3.141....

The circumference = π * diameter = 2πr


Trigonometry

“Trigonometry” means triangle measurement, but it’s really about angles. You have an angle then add an imaginary line to close the open angle creating a tri-angle. Image slicing down directly vertical creating a right angle.

SOH-CAH-TOA + Reciprocals

Not matter what right angle triangle you have with a certain degree, lets say a right angle triangle with the hypotenuse top left and the bottom left angle is 60°, will always be the same result no matter the side lengths. For 60° it will always be the ratio of 0.866..

  • Trig fns are properties of angles, not triangles. Just imagine the triangle to visualise the meaning of the angles.
  • Trig fns are the ratio of 2 lengths.

The 6 trig functions are simply the ratios between the lengths of these 3 sides.

  • Opposite (O): directly across from theta (θ)
  • Hypotenuse (H): directly across from the right angle.
  • Adjacent (A): the remaining side.

Each reciprocal pair starts with “Co”: Co-sine + Secent, Sine + Co-Secant, and Tangent + Co-tangent.

  • sine: sinθ = O / H -> cosecant: cscθ = H / O
  • cosine: cosθ = A / H -> secant: secθ = H / A
  • tangent: tanθ = O / A -> cotangent: cotθ = A / O

If we only have θ and the hypotenuse, that is 1 then:

  1. sinθ = Opp
  2. cosθ = Adj
  3. tanθ = Opp / Adj = sinθ / cosθ

Pythagorean Theorem

Area of a right-angle triangle: Adj^2 * Opp^2 = Hyp^2


Limits

Limit is the value being appraoched. It is not the same as a the function’s value. However, the limit does not always exist (DNE) if the graph splits in 2 (ending 1st graph and starting on 2nd graph different spots)

calc-limit

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