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://literaturetime.com.

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://literaturetime.com.

78FA82CD-C27A-4F7D-8A29-9F1A4B265AF7
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:

The law in one frame of reference or time period is not the law in another frame of reference or time period. The law changes over space and time. The law is not absolute. The law is relative. The law is flexible.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s