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 are the solutions to your problems. a) Complete the table for values of y = 2 x and y = 3 x, correct to 1 decimal place. Step 1: Calculate values for y = 2 x. For x = 0^, y = 2 0^ = 2(1) = 2.0. For x = 30^, y = 2 30^ = 2(sqrt(3)2) = sqrt(3) ≈ 1.7. For x = 60^, y = 2 60^ = 2((1)/(2)) = 1.0. For x = 90^, y = 2 90^ = 2(0) = 0.0. For x = 120^, y = 2 120^ = 2(-(1)/(2)) = -1.0. For x = 150^, y = 2 150^ = 2(-sqrt(3)2) = -sqrt(3) ≈ -1.7. For x = 180^, y = 2 180^ = 2(-1) = -2.0. For x = 210^, y = 2 210^ = 2(-sqrt(3)2) = -sqrt(3) ≈ -1.7. For x = 240^, y = 2 240^ = 2(-(1)/(2)) = -1.0. For x = 270^, y = 2 270^ = 2(0) = 0.0. For x = 300^, y = 2 300^ = 2((1)/(2)) = 1.0. For x = 330^, y = 2 330^ = 2(sqrt(3)2) = sqrt(3) ≈ 1.7. For x = 360^, y = 2 360^ = 2(1) = 2.0. Step 2: Calculate values for y = 3 x. For x = 0^, y = 3 0^ = 3(0) = 0.0. For x = 30^, y = 3 30^ = 3((1)/(2)) = 1.5. For x = 60^, y = 3 60^ = 3(sqrt(3)2) ≈ 2.6. For x = 90^, y = 3 90^ = 3(1) = 3.0. For x = 120^, y = 3 120^ = 3(sqrt(3)2) ≈ 2.6. For x = 150^, y = 3 150^ = 3((1)/(2)) = 1.5. For x = 180^, y = 3 180^ = 3(0) = 0.0. For x = 210^, y = 3 210^ = 3(-(1)/(2)) = -1.5. For x = 240^, y = 3 240^ = 3(-sqrt(3)2) ≈ -2.6. For x = 270^, y = 3 270^ = 3(-1) = -3.0. For x = 300^, y = 3 300^ = 3(-sqrt(3)2) ≈ -2.6. For x = 330^, y = 3 330^ = 3(-(1)/(2)) = -1.5. For x = 360^, y = 3 360^ = 3(0) = 0.0. The completed table is: |c|c|c|c|c|c|c|c|c|c|c|c|c|c| x^ & 0^ & 30^ & 60^ & 90^ & 120^ & 150^ & 180^ & 210^ & 240^ & 270^ & 300^ & 330^ & 360^ \\ y = 2 x & 2.0 & 1.7 & 1.0 & 0.0 & -1.0 & -1.7 & -2.0 & -1.7 & -1.0 & 0.0 & 1.0 & 1.7 & 2.0 \\ y = 3 x & 0.0 & 1.5 & 2.6 & 3.0 & 2.6 & 1.5 & 0.0 & -1.5 & -2.6 & -3.0 & -2.6 & -1.5 & 0.0 \\ 3 done, 2 left today. You're making progress.