# Question 25: Trigonometric equations. (Late Middle Palaeolithic).

QUESTION 25.

TRIGONOMETRIC EQUATIONS (Late Middle Palaeolithic).

θ = s/60 × 2π

8sin^2(θ) + 2sin(θ) – 1 = 0

2cos^2(θ) + √3cos(θ) = 0

a. Solve for θ and s. (Note: there are several possible θ values, find the specific angle that corresponds to both sine and cosine).

8sin^2(θ) + 4sin(θ) – 2sin(θ) – 1 = 0

4sin(θ)(2sin(θ) + 1) – 1(2sin(θ) + 1) = 0

(2sin(θ) + 1) (4sin(θ) – 1) = 0

2sin(θ) + 1 = 0

2sin(θ) = -1

sin(θ) = -1/2

4sin(θ) – 1 = 0

4sin(θ) = 1

sin(θ) = 1/4

cos(θ)(2cos(θ) + √3) = 0

cos(θ) = 0 or 2cos(θ) + √3 = 0

cos(θ) = 0 or cos(θ) = -√3/2

sin^-1(-1/2) = π – θ = π/6

θ = π – sin^-1(-1/2) = 7π/6

cos^-1(-√3/2) = 2π – θ = 5π/6

θ = 2π – cos^-1(-√3/2) = 7π/6

7π/6 = s/60 × 2π

7/12 = s/60

s = 7/12 × 60 = 35

b. Re-divide s by 60 to get s/60. Then choose k for minutes (m) and add k + s/60 to get m. Then divide m by 60 and choose k for hours (h) then add k + m/60 to get h. Then divide h by 24 and choose k for days (d) then add k + h/24 to get d. Then divide d by 30 and choose k for months (M) then add k + d/30 to get M. Then divide M by (73/6) and choose k for years (y) then add k + M/(73/6) to get y.

Tip: choose a meaningful k for years (y), especially if you have sinned, such as the Late Middle Palaeolithic, 60,000 to 35,000 years ago. For example, if you are a cannibal, this is a place and time where you can find relative innocence. For a full understanding of this read https://crimetravel.co.uk.

s/60 = 35/60 = 7/12

k = m – s/60 = 39

m = k + s/60 = 475/12

m/60 = 95/144

k = h – m/60 = 19

h = k + m/60 = 2831/144

h/24 = 2831/3456

k = d – h/24 = 23

d = k + h/24 = 82319/3456

d/30 = 82319/103680

k = M – d/30 = 7

M = k + d/30 = 808079/103680

M/(73/6) = 808079/1261440

k = y – M/(73/6) = 50350

y = k + M/(73/6) = 63514312079/1261440

c. Choose and workout the magnitudes of T^1, T^-1, T^2 and T^-2, also workout t, A and B.

T^1 = √(A/B) = 10^18 as

T^-1 = √(B/A) = 10^-18 Es

T^2 = A/B = 10^36 as²

T^-2 = B/A = 10^-36 Es²

t = A/T^1 = y × 31536000 = 1.587857801975 × 10^12 s

A = tT^1 = X × 10^12 × 10^18 = X × 10^30 as

B = A/T^2 = X × 10^30 / 10^36 = X × 10^-6 Es

d. Although you have done it forward or ascending, undo or reverse-workout the integers and decimals of the different time units backward or descending.

M/(73/6) = y – k = 808079/1261440

M = (y – k) × (73/6) = 808079/103680

k = M – d/30 = 7

d/30 = M – k = 82319/103680

d = (M – k) × 30 = 82319/3456

k = d – h/24 = 23

h/24 = d – k = 2831/3456

h = (d – k) × 24 = 2831/144

k = h – m/60 = 19

m/60 = h – k = 95/144

m = (h – k) × 60 = 475/12

k = m – s/60 = 39

s/60 = m – k = 7/12

s = (m – k) × 60 = 35

e. Check months with days.

y – d/365 = t / 31536000 – d/365 = 50350

d – h/24 = (y – k) × 365 – h/24 = 233

h – m/60 = (d – k) × 24 – m/60 = 19

m – s/60 = (h – k) × 60 – s/60 = 39

s – cs/100 = (m – k) × 60 – cs/100 = 35

50350 years 233 days 19:39:35

50350 years 7 months 23 days 19:39:35

Hand written example:

The Late Middle Paleolithic, about 60,000 to 35,000 years ago. Again, for example, if you are a cannibal, this is a place and time where you can find relative innocence. For a full understanding of this read https://crimetravel.co.uk. Neanderthals in summer, artwork. Like modern humans, Neanderthals (Homo neanderthalensis) are members of the Homo genus. They inhabited Europe and western Asia between 230,000 and 29,000 years ago. https://www.thoughtco.com/beginners-guide-to-the-middle-paleolithic-171839 ## Author:Technical compassion.

Consider compassion, how can Australopithecus or Lower Palaeolithic man be compassionate toward animals, when they themselves were not yet masters of the animal kingdom or even worse still prey themselves? It is impossible, compassion simply did not exist. Compassion is technical, in that you must, for instance, first attain advanced weapons, technologies and infrastructure such as gunpowder, muskets, rifles, nuclear weapons, automobiles, militaries, police, emergency services, roads, buildings, bridges and skyscrapers etc before you can be compassionate toward animals. It is not a case of hey compassion for compassion’s sake like the Buddha. Compassion is not free of charge, it is a definite and tangible deal or bargain. Only now that I am invincibly safe and secure from wild animals in my city, town or fortress and surrounded by guns, and now that I have an overabundance and surplus of food, energy and resources etc can or will I be compassionate toward animals. It is like saying to ‘bear’ “I have a nuke now, therefore I am compassionate toward you.” This is something bear will never understand, in that it is ironic that once you attain nuclear weapons that you are therefore by definition compassionate toward animals. To reiterate, compassion is something technical, it is only attained through a collective effort, through taming the wild and through civilisation. You can only be compassionate once there is no competition.