Question

Describe the graph of the function in terms of a basic trigonometric function. Locate the vertical asymptotes and graph two periods of the function: a. y=-cot 3x
b. y=sec3x
c. y=csc2x

Answer 1

I was not here for the lesson and I need help with how to do this. Please help.

Answer 2

sec(x) = 1/cos(x) Period should be closely related. In particular, vertical asymptotes of sec(x) will coincide with zeros of cos(x)

csc(x) = 1/sin(x) Exactly the same things can be said of this relationship that just were said of sec(x) and cos(x).

cot(x) = cos(x)/sin(x) is a little trickier unti you see that cot(x) = cos(x)/sin(x) = cos(x)*csc(x) and this nicely identifies vertical asymptotes since we just looked as the cosecant.

cos(3x) period modification is a thought process. In this case, comparing to cos(x), everything happens 3-times faster in cos(3) thus, the period is shortened.