A+ SOLUTIONS FOR THE FOLLOWING QUESTIONS

Trigonometric Functions and Graphs

Graphing Trigonometric Equations

Unit Summative Assessment

The following questions are to be answered with full solutions. Be sure to focus on proper mathematical form, including:

Assessment OF Learning: Trig Functions Mid Unit Assignment

1.Using proper graphing techniques, graph the functions given below. Be sure to show all work. (12 marks)

a.y = 3cos2x + 1 for 0 table below you are asked to find the slope of the secant to the function f(x) = tan2x + 1 between two points. Note that the x-coordinate for the second point is just the x-coordinate of the first point plus a small quantity, and that this small quantity becomes 5 times smaller in each row. Complete the table. You only need to show the work for the first two rows. (4 marks)

x1y1x2y2Secant slope

3 /83 /8 + /8

3 /83 /8 + /40

3 /83 /8 + /200

3 /83 /8 + /1000

b.Use the information from part a) to determine the slope of the tangent to the given function at x = 3 /8. (2 marks)

4.The graph below shows the motion of the pedal of a bicycle during 10 seconds of movement.

a.Identify the function and state its period. What does the period represent in this situation? (3 marks)

b.If the above graph represents an adults bicycle, sketch a similar graph to represent the motion of the pedal on a bike belonging to a young child. (3 marks)

5.What is a vertical asymptote and where do they occur for a cosecant function? (3 marks)

6.Outline the process of a secant line becoming a tangent line to a curve. (2 marks)