To determine the five key points, you want to determine he x-coordinates of each quarter period.

For example, to graph a function in the form y = sin(Bx+C), you want to set Bx + C equal to 0, pi/2, pi, 3pi/2, and 2 pi to determine the new x-coordinates that you will use in your graphs.

Sketch a detailed graph for each of the following functions. Graph at least one full period, indicating the coordinates of any key points, and the location of any vertical asymptotes.

1.) y = 2 cos(2x – pi/4)

2.) y = 4 sin(3x + 2pi/4)

3.) y = 3 tan(2x – pi/6)

4.) y = 2 csc(2x – pi/4)

5.) y = 5 sec(1/2x – pi/3)

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