ElectricPavlov

Seems an odd question, but here ya go:    611.97/50.98 x 100% = 1200.41 %

Slope = rise / run    = (4-7)/(-2-5) = -3/(-7) = 3/7

pH = -log[h3o] =  - log[.0088] = 2.056

'theta'   is gennerally used as an unknown angle   like   sin(theta) = 2/3      much the way 'x' is used as an unknown variable in an equation: x + 3 = 5

10   

When you are attempting to crawl across the tracks.  Provided you have a train schedule, an accurate watch, you know how far you are from the trains' departure AND the trains are running on schedule AND you know how fast they are travelling !    LOL

Volume(n) = 22 + (2/25)(tf-t0)           If 2/25 is a liter measurement

Volume(n) =  22 (1 +2/25(tf-t0))        If 2/25 is a FACTOR   in the question      ....  the question is unclear  (I suspect the second equation is the correct one)

OK...it is a right triangle with a hypotenuse of 30 feet       the angle = 32 degrees        sin (32) = OPPOSITE/HYPOTENUSE    ((Remember 'SOHCAHTOA' ?)

So sin(32) = .5299  (by calculator)  =  opposite/hypotenuse

.5299 = opposite/30

.5299 (30) = opposite =  15.897 feet in elevation  

Arcsin(theta) = Arcsin(1/3) = theta = 19.47 degrees          then just use calculator to find cot(19.47) = 2.828

Sorry ...didn't see 'EXACT' in your post

sin(theta) = 1/3           cos^2 (theta) =  (1-sin^2)

                                                          = 1-1/9 = 8/9

                                    cos theta = sqrt (8/9)=  2sqrt2  /  3 

COT(theta) = cos/sin   =   (2sqr2 / 3) /  1/3  =     2sqrt2 / 3  x  3/1  = 2 sqrt2

First find 'x'

Arcsin(x) = Arcsin (1/2) = 30 degrees    now you can just use the calculator to find   cos(30) = .866    and tan(30) = .577