CPhill

You're on the right track....just a calculator problem....

On the home page calculator....make sure you're in DEGREE Mode....[at bottom left ]

Key in 

14.6 / 7.2  

Then....hit the  "2nd button"

You will see the  "atan" button....hit that

Then hit "="

You should see   "63.749....."

This where   "63.7"   comes from.....

Hope that helps.....incidentally..."atan"  is the same as "tan^-1 ".....it means "tangent inverse"

Note that  tan (2pi - x)  =

sin (2pi - x)          sin2pi * cosx - cos2pi *sinx

_________  =    _______________________  =

cos (2pi - x)       cos2pi *cosx + sin 2pi * sinx

- sin x

_____   =  

 cos x

- 2 / sqrt (29)

___________   =

  5 / sqrt (29)

-2/5

Just as PM found.......!!!!

Note that   if

(x + 7) (x - 1)  = 0

Then  either  x + 7  = 0     which implies that x =   -7  makes this true...so this is a root

OR

x - 1  = 0     which implies that  x =  1  makes this true.......so this is also a root

OK....not too much here

(x + 7) ( x - 1) = 0

x^2 + 7x - 1x  - 7   = 0

x^2 + 6x - 7  = 0

Just  n

We have n  things and we want to choose just 1

n ways to do that   !!!

OK.....!!!!

YOU GOT IT>>>>>GREAT JOB>>>>!!!!!

This was/is an interesting one.....!!!

Nope, PM....your method is just as good   (and maybe better) than mine...!!!

Note that   

i^1 + i^2 + i^3 + i^4   =

i - 1 - i + 1   =  0

And  each of the 4   successive  terms have the same pattern and  will also sum to 0

So......  i^1 to i^96 inclusive will have a sum of 0 

So

i^97 = i

i^98 = -1

i^99 = - i

So...the sum  is just  -1

Very nice, EP!!!