# 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`

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- 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:

`sinθ = Opp`

`cosθ = Adj`

`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)

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