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
Here is the solution. 6. Given () = 4/5 and is in the first quadrant, find (2) and (2). Step 1: Find (). Since is in the first quadrant, () is positive. () = sqrt(1 - ^2()) = sqrt(1 - ((4)/(5))^2) = sqrt(1 - (16)/(25)) = sqrt((25-16)/(25)) = sqrt((9)/(25)) = (3)/(5) Step 2: Find (2). Use the double angle formula (2) = 2()(). (2) = 2 ((4)/(5)) ((3)/(5)) = (2 × 4 × 3)/(5 × 5) = (24)/(25) Step 3: Find (2). Use the double angle formula (2) = ^2() - ^2(). (2) = ((3)/(5))^2 - ((4)/(5))^2 = (9)/(25) - (16)/(25) = (9-16)/(25) = -(7)/(25) The final answers are (2) = (24)/(25) and (2) = -(7)/(25).