Exam 28: Graphs of Other Trigonometric Functions

Consider the functions given by​ $f ( x ) = 2 \sin x$ $and$ $g ( x ) = \frac { 1 } { 2 } \csc x$ on the interval (0,π). Describe the behavior of each of the functions as x approaches π. ​

Consider the function given by​ $y=x-\cos x$ ​ Use a graphing utility to select the graph of the function. ​

Determine whether the function below is even,odd,or neither.​ $f ( x ) = 3 \sec x$ ​

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound.​ $f ( x ) = 2 ^ { - x / 4 } \cos x$ ​ ​

Use a graphing utility to select the graph of the function below.Describe the behavior of the function as x approaches 0. ​​ $f ( x ) = x \cos \frac { 1 } { x }$

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.​ $g ( x ) = 3 e ^ { - \frac { x ^ { 2 } } { 2 } } \sin x$ ​

Use a graphing utility to select the graph of the function​ $y = \frac { 6 } { x } + \cos x , x > 0$ ​ ​

Describe the behavior of the function below as x approaches zero.​ $f ( x ) = \frac { | x | } { 5 } \cos ( x )$ ​

Select the graph of the given function.Make sure to include at least two periods.​ $y = \csc 2 x$ ​

State the period of the function: ​​ $y = \tan \frac { x } { 3 }$ ​

Describe the behavior of the function below as x approaches zero.​ $f ( x ) = | 5 x \cos x |$ ​