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 = (9)/(5) into the identity. ((9)/(5))^2 + ^2 = 1 Step 2: Square the term and simplify. (81)/(25) + ^2 = 1 Step 3: Isolate ^2 . ^2 = 1 - (81)/(25) To subtract, express 1 as (25)/(25): ^2 = (25)/(25) - (81)/(25) ^2 = (25 - 81)/(25) ^2 = -(56)/(25) Step 4: Analyze the result. The square of any real number, including , cannot be negative. Since ^2 = -(56)/(25) is a negative value, there is no real value for that satisfies this equation. Additionally, the value = (9)/(5) (which is 1.8) is outside the valid range for the sine function. The sine of any real angle must be between -1 and 1 (inclusive), i.e., -1 1. Since (9)/(5) > 1, there is no real angle for which = (9)/(5). Therefore, no such acute angle exists. Given the impossible condition, it is not possible to find a real value for .