Question 16: Trigonometry and radians.

QUESTION 16.

Note: if you want to create your own trigonometry questions, to save you time, θ or M/(73/6) × 360 should have at least 2 decimal places, otherwise, there are 0 seconds. And 3 decimal places is recommended as the maximum.

Note: radians are very hard, you basically must have the Mathway app to make light work of fractions and radians, also a second scrap piece of paper is recommended.

Question 16:

(TRIGONOMETRY AND RADIANS).

T^1 = √(A/B) = 10^12 ps

k = y – M/(73/6) = 81073

sin(M(73/6) × 2π) = -0.9260024197156

cos(M(73/6) × 2π) = -0.3775175740026

a. What are the magnitudes of T^-1, T^2 and T^-2?

b. Workout θ.

c. Workout M/(73/6) and the other decimal remainders and integers (k) of the months, days, hours, minutes and seconds.

d. What is the total value of y?

e. What are the values of t, A and B?

f. Check the days and months.

a.

T^-1 = √(B/A) = 10^-12 Ts

T^2 = A/B = 10^24 ps²

T^-2 = B/A = 10^-24 Ts²

b.

sin^-1(-0.9260024197156) = -3391π/9000

cos^-1(-0.3775175740026) = 5609π/9000

θ = π + 3391π/9000 = 12391π/9000

or

θ = 2π – 5609π/9000 = 12391π/9000

c.

M/(73/6) = (12391π/9000)/2π = 12391/18000

M = M/(73/6) × (73/6) = 904543/108000

k = M – d/30 = 8

d/30 = M – k = 40543/108000

d = (M – k) × 30 = 40543/3000

k = d – h/24 = 11

h/24 = d – k = 943/3600

h = (d – k) × 24 = 943/150

k = h – m/60 = 6

m/60 = h – k = 43/150

m = (h – k) × 60 = 86/5

k = m – s/60 = 17

s/60 = m – k = 1/5

s = (m – k) × 60 = 12

d.

y = k + M/(73/6) = 1459326391/18000

e.

t = A/T^1 = y × 31536000 = 2.556739837032 × 10^12s

A = tT^1 = X × 10^12 × 10^12 = X × 10^24 ps

B = A/T^2 = X × 10^24 / 10^24 = X Ts

f.

y – d/365 = t / 31536000 – d/365 = 81073

d – h/24 = d/365 × 365 – h/24 = 251

h – m/60 = h/24 × 24 – m/60 = 6

m – s/60 = m/60 × 60 – s/60 = 17

s – cs/100 = s/60 × 60 – cs/100 = 12

NOTE: obviously we do NOT literally minus the decimal such as s/60 on the calculator, we simply minus the integers (k) and multiply the decimal by (73/6), 30, 24 or 60. We do not write or type long numbers. We only have to type the first division below and ‘lift’ the whole number, the rest is done by the calculator.

For example:

Note: you do not need to write the below, it is all done on the calculator.

y – d/365 = 2556739837032 / 31536000 – d/365 = 81073

d – h/24 = (81073.6883888889 – 81073) × 365 – h/24 = 251

h – m/60 = (251.26194444274 – 251) × 24 – m/60 = 6

m – s/60 = (6.28666662576143 – 6) × 60 – s/60 = 17

s – cs/100 = (17.1999975456856 – 17) × 60 – cs/100 = 12

t = 81073 years 251 days 06:17:12

Hand written example:

A4277A34-1D3B-4A6D-9A71-905726079058

Author:

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.

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