Solve the following trigonometric equations graphically for 0^ leq x leq 360^ : a) x = 0.71 b) x = 0.31

To solve this problem, first, you need to draw the graph of y = x for 0^ x 360^. Step 1: Draw the graph of y = x. • Draw a coordinate plane with the x-axis from 0^ to 360^ and the y-axis from -1 to 1. • Plot the key points for the sine function: • (0^, 0) • (90^, 1) (maximum value) • (180^, 0) • (270^, -1) (minimum value) • (360^, 0) • Connect these points with a smooth curve to form the sine wave. Step 2: Use the graph to solve the equations. To solve x = k using the graph, draw a horizontal line at y = k. The x-coordinates of the intersection points of this line with the sine curve are the solutions for x. a) x = 0.71 Draw a horizontal line at y = 0.71. Find the x-values where this line intersects the graph of y = x. The principal value is x = (0.71) ≈ 45.2^. The second solution in the range 0^ x 360^ is x = 180^ - 45.2^ = 134.8^. The solutions are approximately x = 45.2^, 134.8^. b) x = 0.31 Draw a horizontal line at y = 0.31. Find the x-values where this line intersects the graph of y = x. The principal value is x = (0.31) ≈ 18.1^. The second solution is x = 180^ - 18.1^ = 161.9^. The solutions are approximately x = 18.1^, 161.9^. c) x = 0.6 Draw a horizontal line at y = 0.6. Find the x-values where this line intersects the graph of y = x. The principal value is x = (0.6) ≈ 36.9^. The second solution is x = 180^ - 36.9^ = 143.1^. The solutions are approximately x = 36.9^, 143.1^. d) x = -0.81 Draw a horizontal line at y = -0.81. Find the x-values where this line intersects the graph of y = x. First, find the reference angle: = (0.81) ≈ 54.1^. Since x is negative, the solutions are in the third and fourth quadrants. The solution in the third quadrant is x = 180^ + 54.1^ = 234.1^. The solution in the fourth quadrant is x = 360^ - 54.1^ = 305.9^. The solutions are approximately x = 234.1^, 305.9^. That's 2 down. 3 left today — send the next one.