Complete the table and draw the graphs for y = 2 extcos x and y = 3 extsin x for x from 0^ exto to 360^ exto in intervals of 30^ exto.

Step 1: Complete the table for values of y = 2 x and y = 3 x. We need to calculate the missing values for y = 2 x at x = 240^ and for y = 3 x at x = 270^, correct to 1 decimal place. For y = 2 x: At x = 240^: y = 2 (240^) = 2 × (-(1)/(2)) = -1.0 For y = 3 x: At x = 270^: y = 3 (270^) = 3 × (-1) = -3.0 The completed table is: | x^ | 0^ | 30^ | 60^ | 90^ | 120^ | 150^ | 180^ | 210^ | 240^ | 270^ | 300^ | 330^ | 360^ | |---|---|---|---|---|---|---|---|---|---|---|---|---|---| | y = 2 x | 2 | 1.7 | 1 | 0 | -1.0 | -1.7 | -2.0 | -1.7 | -1.0 | 0 | 1.0 | 1.7 | 2 | | y = 3 x | 0 | 1.5 | 2.6 | 3 | 2.6 | 1.5 | 0 | -1.5 | -2.6 | -3.0 | -2.6 | -1.5 | 0 | Step 2: Draw the graph of y = 2 x and y = 3 x. a) Set up the axes on the provided grid. The x-axis should represent angles from 0^ to 360^. A suitable scale would be 2 \, cm for 30^. b) The y-axis should represent values from approximately -3.0 to 3.0. A suitable scale would be 2 \, cm for 1 unit. c) Plot the points from the completed table for y = 2 x and draw a smooth curve through them. Label this curve y = 2 x. d) Plot the points from the completed table for y = 3 x and draw a smooth curve through them. Label this curve y = 3 x. Step 3: Use the graph to find the values of x when 2 x - 3 x = 0. The equation 2 x - 3 x = 0 can be rewritten as 2 x = 3 x. This means we need to find the x-coordinates of the intersection points of the two graphs, y = 2 x and y = 3 x. From the graph, locate the points where the two curves intersect. The intersection points occur at approximately: x ≈ 33.7^ and x ≈ 213.7^ Step 4: Use the graph to find the values of y when 2 x = 3 x. This asks for the y-coordinates of the intersection points found in Step 3. At x ≈ 33.7^, read the corresponding y-value from either graph. y = 2 (33.7^) ≈ 1.66 ≈ 1.7 y = 3 (33.7^) ≈ 1.66 ≈ 1.7 At x ≈ 213.7^, read the corresponding y-value from either graph. y = 2 (213.7^) ≈ -1.66 ≈ -1.7 y = 3 (213.7^) ≈ -1.66 ≈ -1.7 The values of y are approximately 1.7 and -1.7. Last free one today — make it count tomorrow, or type /upgrade for unlimited.