CPhill

sin(3theta) - 4 = -3       add 4 to both sides

sin(3theta)  = 1

sin (theta)  = 1    at    90° + n360°

So.....dividing this angle by 3, theta  = 30°+ n120°

1.  Remember that sin^x + cos^x  = 1

So

[ sin^x + cos^x] / cos x   =

1 /  cos x  =

sec x    .....     and this equals the right hand side

2.  Remember that...... 1  + tan^2x   = sec^2x    .......so

1 +  1/2   =   sec^2x

3/2   = sec^2x

[+/-] sqrt (3/2)  = sec x

Melody....the shaded bit is the area inside the large circle that is not occupied by the seven smaller circles........I had a good GeoGebra presentation of it.....but......I can't upload any pics.....{BOO !!!]

Some claim it was an Anonymous Cow whose name is lost to History.......others claim it was the obscure figure, Cal Cium.......yet, others attribute it to the little-known scientist, Lewis Pasture.

The latter seems most likely..........

The adjacent side will be 98.1 as well......both angles opposite these sides will be 45°.....  and in any triangle, when two angles are equal, the sides opposite these angles are equal as well.

Let the unit digit = x

Then, the tens digit  = 3x

And we have the following equation

[3x(10)  + x]   - 54  =  [ x(10) + 3x ]  simplify

30x + x   -   54   =  10x + 3x

31x - 54  = 13 x

18x  - 54  = 0

18x  = 54      divide both sides by 18

x  = 3         and 3x  = 3(3)   = 9

So

The larger number  is  3(3)(10) + 3   = 93

And the smaller number  is  10(3) + 3(3)  =  39

And their difference = 54

Just as Anonymous4338 found  !!!!!!

Here is a graphical solution........https://www.desmos.com/calculator/jdhw9qrzoa

The general solution appears to be about  36.9° + n360°  whrere n is some integer

(sin x - sin y) / (cos x - cos y) = - cot ((x+y)/2)

( 2cos[(x + y)/2]*sin [(x - y)/2] )  /  ( -2sin [(x + y)/2 ]* sin [(x - y)/2] ) =

2cos[(x + y)/2] / -2sin [(x + y)/2]  =

- (cos[(x + y)/2] / sin [(x + y)/2] )=

- cot [ (x + y)/2 ]

6-2 (3x-5) = -26  simplify

6 -6x + 10   = -26

16 - 6x  = -26       subtract 16 from both sides

-6x  = - 42           divide both sides by -6

x = 7

1.09 x 10^-2   =  0.0109