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a million) As x is in [0, 2?), 4x is in [0, 8?). consequently, there are 4 classes and in each era of length 2?, there'll be 2 suggestions for the given function; through fact sin is helpful in first and 2nd quadrants. As such in entire there'll be 8 suggestions relaxing sin(4x) = ?3/2. 2) sin(4x) = ?3/2, implies, 4x = ?/3 many times as sin is helpful in 1st & 2d quadrants, 4x = n? + {(-a million)^n}*(?/3) Plugging n = 0, a million, 2, ---, 7, we get 4x = {?/3, 2?/3, 7?/3, 8?/3, 14?/3, 19?/3, 20?/3} consequently x = {?/12, ?/6, 7?/12, 2?/3, 7?/6, 19?/12, 5?/3}