Answer:
x = 29° + n·120° . . . or . . . 261° +n·360° . . . . for any integer n
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
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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.
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The graph shows solutions to sin(x-3)-cos(2x+6)=0, which has the same solutions as the given equation.