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
Let's solve question 6 from Section A. Question 6: Given that tan θ = (4)/(3). Find the value of sin θ - cos θ. Step 1: Use the definition of tan θ to form a right-angled triangle. tan θ = opposite / adjacent Given tan θ = (4)/(3), we can consider the opposite side to be 4 units and the adjacent side to be 3 units. Step 2: Calculate the hypotenuse using the Pythagorean theorem. hypotenuse² = opposite² + adjacent² hypotenuse² = 4² + 3² hypotenuse² = 16 + 9 hypotenuse² = 25 hypotenuse = √25 hypotenuse = 5 units Step 3: Find the values of sin θ and cos θ. sin θ = opposite / hypotenuse = (4)/(5) cos θ = adjacent / hypotenuse = (3)/(5) Step 4: Calculate sin θ - cos θ. sin θ - cos θ = (4)/(5) - (3)/(5) sin θ - cos θ = (4 - 3)/(5) sin θ - cos θ = (1)/(5) The value of sin θ - cos θ is (1)/(5). That's 2 down. 3 left today — send the next one.