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: Find the value of . Given = (3)/(5). Using the Pythagorean identity ^2 + ^2 = 1: ^2 + ((3)/(5))^2 = 1 ^2 + (9)/(25) = 1 ^2 = 1 - (9)/(25) ^2 = (25)/(25) - (9)/(25) ^2 = (16)/(25) Taking the square root, we get: = ± sqrt((16)/(25)) = ± (4)/(5) Assuming is an acute angle (in the first quadrant), is positive. = (4)/(5) Step 2: Simplify (90^ - ). Using the complementary angle identity, (90^ - ) = . Step 3: Find the value of . We know that = ( )/( ). Substitute the values of and : = (3)/(5)(4)/(5) = (3)/(4) Step 4: Substitute the values into the expression - (90^ - ). The expression becomes: Substitute the values found in Step 1 and Step 3: (4)/(5) - (3)/(4) Step 5: Calculate the final value. To subtract the fractions, find a common denominator, which is 20: (4 × 4)/(5 × 4) - (3 × 5)/(4 × 5) (16)/(20) - (15)/(20) (16 - 15)/(20) (1)/(20) The final answer is: (1)/(20) That's 2 down. 3 left today — send the next one.