QUESTION 15.

(TRIGONOMETRIC).

T^1 = √(A/B) = 10^15 fs

k = y – M/(73/6) = 4623

sin(M(73/6) × 360) = -0.3050305188087

cos(M(73/6) × 360) = 0.95234257627983

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 answer.

a.

T^-1 = √(B/A) = 10^-15 Ps

T^2 = A/B = 10^30 fs²

T^-2 = B/A = 10^-30 Ps²

b.

sin^-1(-0.3050305188087) = -17.76°

cos^-1(0.95234257627983) = 17.76°

θ = 360 – 17.76 = 342.24° = 8556/25°

c.

M/(73/6) = (8556/25)/360 = 713/750

M = M/(73/6) × (73/6) = 52049/4500

k = M – d/30 = 11

d/30 = M – k = 2549/4500

d = (M – k) × 30 = 2549/150

k = d – h/24 = 16

h/24 = d – k = 149/150

h = (d – k) × 24 = 596/24

k = h – m/60 = 23

m/60 = h – k = 21/25

m = (h – k) × 60 = 252/5

k = m – s/60 = 50

s/60 = m – k = 2/5

s = (m – k) × 60 = 24

d.

y = k + M/(73/6) = 3467963/750

e.

t = A/T^1 = y × 31536000 = 1.45820908224 × 10^11s

A = tT^1 = X × 10^11 × 10^15 = X × 10^26 fs

B = A/T^2 = X × 10^26 / 10^30 = X × 10^-4 Ps

f.

y – M/(73/6) = t / 31536000 – M/(73/6) = 4623

M – d/30 = M/(73/6) × (73/6) – d/30 = 11

d – h/24 = d/30 × 30 – h/24 = 16

h – m/60 = h/24 × 24 – m/60 = 23

m – s/60 = m/60 × 60 – s/60 = 50

s – cs/100 = s/60 × 60 – cs/100 = 24

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 – M/(73/6) = 145820908224 / 31536000 – M/(73/6) = 4623

M – d/30 = (4623.95066666667 – 4623) × (73/6) – d/30 = 11

d – h/24 = (11.5664444444439 – 11) × 30 – h/24 = 16

h – m/60 = (16.9933333333165 – 16) × 24 – m/60 = 23

m – s/60 = (23.8399999995959 – 23) × 60 – s/60 = 50

s – cs/100 = (50.3999999757542 – 50) × 60 – cs/100 = 24

t = 4623 years 11 months 16 days 23:50:24

Hand written example: