the range is greater then -1 but less than 1
-1<r<1
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It is zero.
sin x can have any value between -1 and 1; therefore, 3 sin x has three times this range (from -3 to 3).
This is the graph of a diagnol line. Range: (-infinity, infinity)
A*sin(x) + cos(x) = 1B*sin(x) - cos(x) = 1Add the two equations: A*sin(x) + B*sin(x) = 2(A+B)*sin(x) = 2sin(x) = 2/(A+B)x = arcsin{2/(A+B)}That is the main solution. There may be others: depending on the range for x.
The multiplication by 3 increases the magnitude, and the + 3 shifts the graph upward to be "centred" at y = 3. The graph now oscillates between 6 and 0 (3 + 3, 3 - 3).