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 for question 1 from the image. 1. Given A = 3. Find the value of (i) A (ii) A (iii) A (iv) A (v) A (In Surd form) Step 1: Use the given A = 3 to construct a right-angled triangle. Since A = oppositeadjacent, we can consider the opposite side to be 3 units and the adjacent side to be 1 unit. Step 2: Use the Pythagorean theorem to find the hypotenuse. Let the opposite side be o=3 and the adjacent side be a=1. Let the hypotenuse be h. h^2 = o^2 + a^2 h^2 = 3^2 + 1^2 h^2 = 9 + 1 h^2 = 10 h = sqrt(10) Step 3: Calculate each trigonometric ratio. (i) A A = oppositehypotenuse = (3)/(sqrt(10)) Rationalize the denominator: A = (3)/(sqrt(10)) × sqrt(10)sqrt(10) = 3sqrt(10)10 The final answer for (i) is 3sqrt(10)10. (ii) A A = adjacenthypotenuse = (1)/(sqrt(10)) Rationalize the denominator: A = (1)/(sqrt(10)) × sqrt(10)sqrt(10) = sqrt(10)10 The final answer for (ii) is sqrt(10)10. (iii) A A = (1)/( A) = (1)/(1)sqrt(10) = sqrt(10) The final answer for (iii) is sqrt(10). (iv) A A = (1)/( A) = (1)/(3)sqrt(10) = sqrt(10)3 The final answer for (iv) is sqrt(10)3. (v) A A = (1)/( A) = (1)/(3) The final answer for (v) is (1)/(3).