Exam 28: Graphs of Other Trigonometric Functions

Use a graphing utility to select the graph of the expression below,making sure to show at least two periods. ​​ $y = \frac { 1 } { 2 } \csc \left( \frac { \pi x } { 3 } - \frac { \pi } { 3 } \right)$ ​

Determine whether the function below is even,odd,or neither.​ $f ( x ) = x ^ { 8 } \cot \frac { x } { 2 }$ ​

Select the graph of the function below.Include two full periods.​ $y = 4 \tan ( x + \pi )$ ​

Use a graphing utility to select the graph of the function below,making sure to show at least two periods.​ $y = \sec \frac { x } { 2 }$ ​​ ​ ​ Xscl = $\frac { \pi } { 2 }$ ​ ​ ​​ Xscl = $\frac { \pi } { 2 }$ ​ ​​ Xscl = $\frac { \pi } { 2 }$ ​ ​ Xscl = $\frac { \pi } { 2 }$

Describe the behavior of the function below as x approaches $- {\frac { \pi } { 2 }}^-$ .​ $f ( x ) = 4 \tan x$ ​

Describe the behavior of the function below as x approaches π^-.​ $f ( x ) = 2 \cot x$ ​

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

State the period of the function:​ $y = - \csc 4 x$ ​

Which of the following functions is represented by the graph below?

Determine whether the function below is even,odd,or neither.​ $f ( x ) = \frac { x ^ { 2 } } { 3 } - 3 \sec x$ ​

Determine whether the function below is even,odd,or neither.​ $f ( x ) = \frac { x } { 4 } + \tan ( x )$ ​

Select the graph of the function below.Include two full periods.​ $y = 4 \csc \pi x$ ​

Select the graph of the given function.Make sure to include at least two periods. $y = - 3 \sec ( x + \pi )$ ​

Describe the behavior of the function below as x approaches 0⁺.​ $f ( x ) = 3 \cot x$ ​

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

Determine whether the function below is even,odd,or neither.​ $y = \frac { 1 } { 7 } \tan x$ ​

A plane flying at an altitude of a miles above a radar antenna will pass directly over the radar antenna (see figure).Let d be the ground distance from the antenna to the point directly under the plane and let x be the angle of elevation to the plane from the antenna. $a = 8$ . ​ (d is positive as the plane approaches the antenna. ) Write d as a function of x.​

The projected monthly sales (in thousands of units)of lawn mowers (a seasonal product)are modeled by​ $S = 71 + 3 t - 40 \cos \left( \frac { \pi t } { 6 } \right)$ ​ where t is the time (in months),with t = 1 corresponding to January.Select the graph of the sales function over 1 year. ​

State the period of the function:​ $y = \frac { 1 } { 2 } \sec \frac { \pi x } { 5 }$ ​

Select the graph of the function below.Include two full periods.​ $y = \tan \frac { \pi x } { 6 }$ ​