CPhill

Answered here :

https://web2.0calc.com/questions/right-efg-has-its-right-angle-at-f-eg-10-and-fg-4#r1

−11π12

2pi - 11pi/12  = 

[24pi]/12 - [11pi]/12  =

13pi/12  *  180/pi  =

(13) (180/12)  =

13 * 15 =

195°  =   15°  in the 3rd quadrant

−23π6

4pi - 23pi/6 =

(24pi)/ 6 - (23pi)/6 =

pi/6  =  30°   in the first quadrant 

7π6

7pi/6  * 180 /pi  =   

7 (180/6) =

7* 30 =

210°

And  210  - 180  = 30°  in the 3rd quadrant 

OK

2sqrt (15)  = sqrt (60)

2sqrt (6)  = sqrt (24)

The  other leg  =    sqrt  [ (sqrt (60))^2  - (sqrt (24))^2 ]  = sqrt  [ 60 - 24 ]  = sqrt (36)  = 6= the longer leg

The larger angle [call it A ] is opposite the longer leg....so we can use the tangent to find this angle

tan A =  6 / sqrt (24)      and using the tangent inverse to find  A

arctan (6/ sqrt (24)) = A   ≈  50.8°

Call the number of  bike rentals  = x

And the number of skate rentals =  20 - x

So

25x   + 20 ( 20 - x)   = 455     simplify

25x + 400 - 20x  = 455

5x + 400 = 455     subtract 400 from both sides

5x  = 55     divide both sides by 5

x  =11   = number of  bike rentals

No  number of centimeters  displays  (for me, anyway  )

Good work, EP    !!!!

Perimeter  =  2 (W + L)

So

312  = 2 (63 + L)     diviede both sides  by 2

156  = 63 + L      subtract 63 from both sides

93  = L

The cotangent function is defined as the length of the side adjacent over the length of the side opposite.

9 / [ sqrt (3) / 2 ]  =

(9/1) * (2 /sqrt 3 )  =

18 / sqrt 3  =

18 sqrt (3 ) / 3  =

6sqrt (3)

2sin x  - 2

This one just makes the sin function twice as "tall" as the normal sine function and shifts it down 2 units

-cos (2x) +1

The 2x    makes the period 1/2 as long as the regular cosine graph

The  "-"  " flips" this over the x  axis

The "1"  shifts this up one unit

Here's the graph of this  : https://www.desmos.com/calculator/wtrtlgunw4

Last one 

Max  = 1

Min =  -3

Period = pi

Frequency = 1 /period =  1/pi

Amplitude  =  [ Max - Min] / 2 =   [ 1 - - 3 ] / 2  = [4] / 2  =  2

Equation of midline....   y = [ Max + Min ] / 2  ......y =  [ 1 - 3] / 2    ....y = -2/2  =  -1

One possible equation  of this function  is

y=  -2cos(2x) -1

Here]s the graph :   https://www.desmos.com/calculator/lk6hffalro