This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: The general solution for = (1)/(2) is = 30^ + 360^ n or = 150^ + 360^ n, where n is any integer. Step 2: Substitute = (5)/(2) . (5)/(2) = 30^ + 360^ n or (5)/(2) = 150^ + 360^ n. Step 3: Solve for . First equation: = (2)/(5) (30^ + 360^ n) = 12^ + 144^ n. Second equation: = (2)/(5) (150^ + 360^ n) = 60^ + 144^ n. Step 4: Apply 0^ < < 180^. For = 12^ + 144^ n: n=0: = 12^ n=1: = 156^ n=2: = 300^ > 180^ n=-1: = -132^ < 0^ For = 60^ + 144^ n: n=0: = 60^ n=1: = 204^ > 180^ n=-1: = -84^ < 0^ Solutions: = 12^, 60^, 156^ 12^, 60^, 156^