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: Isolate ^2. The given equation is: 3^2 - 1 = 0 Add 1 to both sides: 3^2 = 1 Divide by 3: ^2 = (1)/(3) Step 2: Take the square root of both sides. = ±sqrt((1)/(3)) = ±(1)/(sqrt(3)) Step 3: Consider the given range for . The problem specifies that 0^ ≤ ≤ 90^. In this range (the first quadrant), the tangent function is positive. Therefore, we take the positive value: = (1)/(sqrt(3)) Step 4: Find the value of . We know that (30^) = (1)/(sqrt(3)). So, = 30^ This value is within the specified range 0^ ≤ ≤ 90^. The solution is 30^.