Draw the graph of Y=sin(2x+30)=0.8 for 0° to 360.By including line, use your graph to solve
(a). Sin (2x+30)=0.8
(b). Sin (2x+30)-0.5=0
(c). Sin (2x+30)>\2
Unfortunately, as an AI language model, I am not able to draw a graph for you. However, here are the steps to solve the given equations using the graph of y=sin(2x+30):
(a) To solve sin(2x+30)=0.8, first draw the graph of y=sin(2x+30). Then, locate the points on the graph where y=0.8. The x-coordinates of those points will give the possible values of 2x+30. Solve for x by subtracting 30 from each of those values and dividing by 2.
(b) To solve sin(2x+30)-0.5=0, again draw the graph of y=sin(2x+30). Locate the points on the graph where y=0.5 and draw a horizontal line at that level (y=0.5) on the graph. Find the x-coordinates of the points where the graph intersects the horizontal line. Those x-coordinates will give the possible values of 2x+30. Solve for x as in part (a).
(c) To solve sin(2x+30)>0.2, draw the graph of y=sin(2x+30). Shade the portion of the graph where y>0.2. Find the range of x-values in that shaded region and write the solution as an inequality involving 2x+30. Solve for x as in parts (a) and (b).