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: Use the Pythagorean identity ^2 + ^2 = 1. Substitute the given value = (3)/(5) into the identity. ((3)/(5))^2 + ^2 = 1 Step 2: Square the term and simplify. (9)/(25) + ^2 = 1 Step 3: Isolate ^2 . ^2 = 1 - (9)/(25) ^2 = (25)/(25) - (9)/(25) ^2 = (16)/(25) Step 4: Take the square root of both sides to find . = ±sqrt((16)/(25)) = ±(4)/(5) Step 5: Determine the sign of . Since is an acute angle, it lies in the first quadrant (0^ < < 90^). In the first quadrant, both sine and cosine values are positive. Therefore, must be positive. = (4)/(5) The value of is (4)/(5).