If sin(x-3)° / cos(2x+6) = 1, then the value of x is

  x = 29° + n·120° . . . or . . . 261° +n·360° . . . . for any integer n

Step-by-step explanation:

Multiplying by the denominator, the equation becomes ...

  sin((x -3)°) = cos((2x+6)°)

The sine and cosine are equal when ...

  (x -3) + (2x +6) = 90 + n·360 . . . . . for any integer n

  3x +3 = 90 + n·360 . . . . . . . . . collect terms

  x +1 = 30 +n·120 . . . . . . . . . . . .divide by 3

  x = 29 + n·120 . . . . . . . . . . . . . . subtract 1

__

The sine and cosine are also equal when ...

  (x -3) -(2x +6) = 90 + n·360

  -x -9 = 90 +n·360

  x = -99 -n·360

Since n can be any integer, this can also be written as ...

  x = 261 + n·360

Possible values of x include {29, 149, 261, 269} +n·360 for any integer n.

_____

The graph shows solutions to sin(x-3)-cos(2x+6)=0, which has the same solutions as the given equation.

48 / 6 = x

in this case, x will equal the amount of money in each card!

x therefore will be 8.

trent had $8 in each birthday card.