Question 1

Graph the function.
-$y=\sin \frac{4}{3} x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 2

Graph the function.
-$y=-\frac{3}{4} \cos \left(x-\frac{\pi}{3}\right)$

Accepted Answer

A) 
  
B) 
  
C)  
  
D) 
  
A) 
  
B) 
  
C)  
  
D)

Question 3

Graph the function.
-$$y = \sin \left( x + \frac { \pi } { 3 } \right)$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

Solve the problem.
-Suppose that the average monthly low temperatures for a small town are shown in the table.
$\begin{array}{l|llllllllllll}
\text { Month } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \
\hline \text { Temperature }\left({ }^{\circ} \mathrm{F}\right) & 19 & 27 & 38 & 45 & 57 & 62 & 65 & 58 & 51 & 41 & 33 & 25
\end{array}$

Model this data using $f ( x ) = a \sin ( b ( x - c ) ) + d$.

Accepted Answer

A)  $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 42$ 
B)  $f ( x ) = 23 \sin \left( \frac { \pi } { 12 } ( x - 4 ) \right) + 42$ 
C)  $f ( x ) = 42 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 23$ 
D)  $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 42$ 
A)  $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 42$ 
B)  $f ( x ) = 23 \sin \left( \frac { \pi } { 12 } ( x - 4 ) \right) + 42$ 
C)  $f ( x ) = 42 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 23$ 
D)  $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 42$

Question 5

Determine the equation of the graph.
-

Accepted Answer

A)  $y = \sec \left( \frac { 1 } { 2 } x \right)$ 
B)  $y = - \sec \left( \frac { 1 } { 2 } x \right)$ 
C)  $y = \sec 2 x$ 
D)  $y = - \sec 2 x$ 
A)  $y = \sec \left( \frac { 1 } { 2 } x \right)$ 
B)  $y = - \sec \left( \frac { 1 } { 2 } x \right)$ 
C)  $y = \sec 2 x$ 
D)  $y = - \sec 2 x$

Question 6

Find the phase shift of the function.
-$$y = - 2 \sin \left( 2 x - \frac { \pi } { 2 } \right)$$

Accepted Answer

A)  $\frac { \pi } { 4 }$ units to the right 
B)  $2 \pi$ units down 
C)  $2 \pi$ units up 
D)  $\frac { \pi } { 2 }$ units to the left 
A)  $\frac { \pi } { 4 }$ units to the right 
B)  $2 \pi$ units down 
C)  $2 \pi$ units up 
D)  $\frac { \pi } { 2 }$ units to the left

Question 7

Solve the problem.
-The voltage E in an electrical circuit is given by E = 5.7 cos 110πt, where t is time measured in seconds. Find the amplitude.

Accepted Answer

A) 11.4 
B) 5.7 
C) 110π 
D) 110 
A) 11.4 
B) 5.7 
C) 110π 
D) 110

Question 8

Graph the function.
-$y=\frac{2}{3} \cos \left(x-\frac{\pi}{4}\right)$

Accepted Answer

A)  
  
B)  
  
C) 
  
D) 
  
A)  
  
B)  
  
C) 
  
D)

Question 9

Graph the function.
-$y=-\frac{3}{4} \sin \left(x-\frac{\pi}{2}\right)$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 10

The function graphed is of the form y = cos x + c, y = sin x + c, y = cos(x - d), or y = sin(x - d), where d is the least possible
positive value. Determine the equation of the graph.
-

Accepted Answer

A)  $y = \sin ( x - 1 )$ 
B)  $y = \cos ( x + 1 )$ 
C)  $y = \cos x - 1$ 
D)  $y = \sin x - 1$ 
A)  $y = \sin ( x - 1 )$ 
B)  $y = \cos ( x + 1 )$ 
C)  $y = \cos x - 1$ 
D)  $y = \sin x - 1$

Question 11

Graph the function.
-$y=+2 \cos x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Solve the problem.
-Determine the period and frequency of oscillation when a pendulum of length 9 feet is released after being displaced 2 radians. Round constants to 8 decimal places, if necessary.

Accepted Answer

A)  Period $= 2 \pi \sqrt { 3.55555556 } \mathrm { sec }$, frequency $= \frac { 1 } { 2 \pi } \sqrt { 0.28125 }$ cycles per sec 
B)  Period $= 9 \pi \mathrm { sec }$, frequency $= \frac { 1 } { 9 \pi }$ cycles per sec 
C)  Period $= \frac { \pi } { 9 }$ sec, frequency $= \frac { 9 } { \pi }$ cycles per sec 
D)  Period $= 2 \pi \sqrt { 0.28125 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 3.55555556 }$ cycles per sec 
A)  Period $= 2 \pi \sqrt { 3.55555556 } \mathrm { sec }$, frequency $= \frac { 1 } { 2 \pi } \sqrt { 0.28125 }$ cycles per sec 
B)  Period $= 9 \pi \mathrm { sec }$, frequency $= \frac { 1 } { 9 \pi }$ cycles per sec 
C)  Period $= \frac { \pi } { 9 }$ sec, frequency $= \frac { 9 } { \pi }$ cycles per sec 
D)  Period $= 2 \pi \sqrt { 0.28125 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 3.55555556 }$ cycles per sec

Question 13

Graph the function over a one-period interval.
-$y=3+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 14

The function graphed is of the form y = cos x + c, y = sin x + c, y = cos(x - d), or y = sin(x - d), where d is the least possible
positive value. Determine the equation of the graph.
-

Accepted Answer

A)  $\sin \left( x - \frac { \pi } { 4 } \right)$ 
B)  $\sin x - \frac { \pi } { 2 }$ 
C)  $\cos \left( x - \frac { \pi } { 2 } \right)$ 
D)  $\sin \left( x - \frac { \pi } { 2 } \right)$ 
A)  $\sin \left( x - \frac { \pi } { 4 } \right)$ 
B)  $\sin x - \frac { \pi } { 2 }$ 
C)  $\cos \left( x - \frac { \pi } { 2 } \right)$ 
D)  $\sin \left( x - \frac { \pi } { 2 } \right)$

Question 15

Solve the problem.
-A spring with a spring constant of 5 and a 1-unit mass attached to it is stretched $3 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?

Accepted Answer

A)  $\mathrm { s } ( \mathrm { t } ) = \frac { 1 } { 3 } \sin \sqrt { \frac { 1 } { 10 } } \mathrm { t }$ 
B)  $s ( t ) = 3 \sin \sqrt { \frac { 1 } { 5 } } t$ 
C)  $s ( t ) = 3 \sin \sqrt { 5 } t$ 
D)  $\mathrm { s } ( \mathrm { t } ) = 5 \sin \sqrt { 3 } \mathrm { t }$ 
A)  $\mathrm { s } ( \mathrm { t } ) = \frac { 1 } { 3 } \sin \sqrt { \frac { 1 } { 10 } } \mathrm { t }$ 
B)  $s ( t ) = 3 \sin \sqrt { \frac { 1 } { 5 } } t$ 
C)  $s ( t ) = 3 \sin \sqrt { 5 } t$ 
D)  $\mathrm { s } ( \mathrm { t } ) = 5 \sin \sqrt { 3 } \mathrm { t }$

Question 16

The function graphed is of the form y = a tan bx or y = a cot bx, where b > 0. Determine the equation of the graph.
-

Accepted Answer

A)  $y = - \cot 4 x$ 
B)  $y = - 4 \tan x$ 
C)  $y = - \tan 4 x$ 
D)  $y = - 4 \cot x$ 
A)  $y = - \cot 4 x$ 
B)  $y = - 4 \tan x$ 
C)  $y = - \tan 4 x$ 
D)  $y = - 4 \cot x$

Question 17

Match the function with its graph.
-1) $y = \sin x$
2) $y = \cos x$
3) $y = - \sin x$
4) $y = - \cos x$

a)

b)

c)

d)

Accepted Answer

A)  $1 \mathrm { C } , 2 \mathrm {~A} , 3 \mathrm {~B} , 4 \mathrm { D }$ 
B)  $1 \mathrm {~B} , 2 \mathrm { D } , 3 \mathrm { C } , 4 \mathrm {~A}$ 
C)  $1 \mathrm {~A} , 2 \mathrm { D } , 3 \mathrm { C } , 4 \mathrm {~B}$ 
D)  $1 \mathrm {~A} , 2 \mathrm {~B} , 3 \mathrm { C } , 4 \mathrm { D }$ 
A)  $1 \mathrm { C } , 2 \mathrm {~A} , 3 \mathrm {~B} , 4 \mathrm { D }$ 
B)  $1 \mathrm {~B} , 2 \mathrm { D } , 3 \mathrm { C } , 4 \mathrm {~A}$ 
C)  $1 \mathrm {~A} , 2 \mathrm { D } , 3 \mathrm { C } , 4 \mathrm {~B}$ 
D)  $1 \mathrm {~A} , 2 \mathrm {~B} , 3 \mathrm { C } , 4 \mathrm { D }$

Graph the function. - $y=\sin \frac{4}{3} x$ $Graph the function. - y=\sin \frac{4}{3} x$

Graph the function. - $y=-\frac{3}{4} \cos \left(x-\frac{\pi}{3}\right)$ $Graph the function. - y=-\frac{3}{4} \cos \left(x-\frac{\pi}{3}\right)$

Graph the function. - $y = \sin \left( x + \frac { \pi } { 3 } \right)$ $Graph the function. - y = \sin \left( x + \frac { \pi } { 3 } \right)$

Solve the problem. -Suppose that the average monthly low temperatures for a small town are shown in the table. Month 1 2 3 4 5 6 7 8 9 10 11 12 Temperature 19 27 38 45 57 62 65 58 51 41 33 25 Model this data using $f ( x ) = a \sin ( b ( x - c ) ) + d$ .

Determine the equation of the graph. -

Find the phase shift of the function. - $y = - 2 \sin \left( 2 x - \frac { \pi } { 2 } \right)$

Solve the problem. -The voltage E in an electrical circuit is given by E = 5.7 cos 110πt, where t is time measured in seconds. Find the amplitude.

Graph the function. - $y=\frac{2}{3} \cos \left(x-\frac{\pi}{4}\right)$ $Graph the function. - y=\frac{2}{3} \cos \left(x-\frac{\pi}{4}\right)$

Graph the function. - $y=-\frac{3}{4} \sin \left(x-\frac{\pi}{2}\right)$ $Graph the function. - y=-\frac{3}{4} \sin \left(x-\frac{\pi}{2}\right)$

The function graphed is of the form y = cos x + c, y = sin x + c, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine the equation of the graph. -

Graph the function. - $y=+2 \cos x$ $Graph the function. - y=+2 \cos x$

Solve the problem. -Determine the period and frequency of oscillation when a pendulum of length 9 feet is released after being displaced 2 radians. Round constants to 8 decimal places, if necessary.

Graph the function over a one-period interval. - $y=3+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)$ $Graph the function over a one-period interval. - y=3+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)$

The function graphed is of the form y = cos x + c, y = sin x + c, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine the equation of the graph. -

Solve the problem. -A spring with a spring constant of 5 and a 1-unit mass attached to it is stretched $3 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?

The function graphed is of the form y = a tan bx or y = a cot bx, where b > 0. Determine the equation of the graph. -

Trigonometric Functions

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Exam 4: Graphs of the Circular Functions

Graph the function. - y=sin⁡43xy=\sin \frac{4}{3} xy=sin34​x

Graph the function. - y=−34cos⁡(x−π3)y=-\frac{3}{4} \cos \left(x-\frac{\pi}{3}\right)y=−43​cos(x−3π​)

Graph the function. - y=sin⁡(x+π3)y = \sin \left( x + \frac { \pi } { 3 } \right)y=sin(x+3π​)

Solve the problem. -Suppose that the average monthly low temperatures for a small town are shown in the table. Month 1 2 3 4 5 6 7 8 9 10 11 12 Temperature 19 27 38 45 57 62 65 58 51 41 33 25 Model this data using f(x)=asin⁡(b(x−c))+df ( x ) = a \sin ( b ( x - c ) ) + df(x)=asin(b(x−c))+d .

Determine the equation of the graph. -

Find the phase shift of the function. - y=−2sin⁡(2x−π2)y = - 2 \sin \left( 2 x - \frac { \pi } { 2 } \right)y=−2sin(2x−2π​)

Solve the problem. -The voltage E in an electrical circuit is given by E = 5.7 cos 110πt, where t is time measured in seconds. Find the amplitude.

Graph the function. - y=23cos⁡(x−π4)y=\frac{2}{3} \cos \left(x-\frac{\pi}{4}\right)y=32​cos(x−4π​)

Graph the function. - y=−34sin⁡(x−π2)y=-\frac{3}{4} \sin \left(x-\frac{\pi}{2}\right)y=−43​sin(x−2π​)

The function graphed is of the form y = cos x + c, y = sin x + c, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine the equation of the graph. -

Graph the function. - y=+2cos⁡xy=+2 \cos xy=+2cosx

Solve the problem. -Determine the period and frequency of oscillation when a pendulum of length 9 feet is released after being displaced 2 radians. Round constants to 8 decimal places, if necessary.

Graph the function over a one-period interval. - y=3+12cos⁡4(x+π2)y=3+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)y=3+21​cos4(x+2π​)

The function graphed is of the form y = cos x + c, y = sin x + c, y = cos(x - d), or y = sin(x - d), where d is the least possible positive value. Determine the equation of the graph. -

Solve the problem. -A spring with a spring constant of 5 and a 1-unit mass attached to it is stretched 3ft3 \mathrm { ft }3ft and released. What is the equation for the resulting oscillatory motion?

The function graphed is of the form y = a tan bx or y = a cot bx, where b > 0. Determine the equation of the graph. -

Match the function with its graph. -1) y=sin⁡xy = \sin xy=sinx 2) y=cos⁡xy = \cos xy=cosx 3) y=−sin⁡xy = - \sin xy=−sinx 4) y=−cos⁡xy = - \cos xy=−cosx a) b) c) d)

Trigonometric Functions

Acute Angles and Right Triangles

Radian Measure and the Unit Circle

Trigonometric Identities

Inverse Circular Functions and Trigonometric Equations

Applications of Trigonometry and Vectors

Complex Numbers, Polar Equations, and Parametric Equations

Filters

Graph the function. - $y=\sin \frac{4}{3} x$ $Graph the function. - y=\sin \frac{4}{3} x$

Graph the function. - $y=-\frac{3}{4} \cos \left(x-\frac{\pi}{3}\right)$ $Graph the function. - y=-\frac{3}{4} \cos \left(x-\frac{\pi}{3}\right)$

Graph the function. - $y = \sin \left( x + \frac { \pi } { 3 } \right)$ $Graph the function. - y = \sin \left( x + \frac { \pi } { 3 } \right)$

Solve the problem. -Suppose that the average monthly low temperatures for a small town are shown in the table. Month 1 2 3 4 5 6 7 8 9 10 11 12 Temperature 19 27 38 45 57 62 65 58 51 41 33 25 Model this data using $f ( x ) = a \sin ( b ( x - c ) ) + d$ .

Find the phase shift of the function. - $y = - 2 \sin \left( 2 x - \frac { \pi } { 2 } \right)$

Graph the function. - $y=\frac{2}{3} \cos \left(x-\frac{\pi}{4}\right)$ $Graph the function. - y=\frac{2}{3} \cos \left(x-\frac{\pi}{4}\right)$

Graph the function. - $y=-\frac{3}{4} \sin \left(x-\frac{\pi}{2}\right)$ $Graph the function. - y=-\frac{3}{4} \sin \left(x-\frac{\pi}{2}\right)$

Graph the function. - $y=+2 \cos x$ $Graph the function. - y=+2 \cos x$

Graph the function over a one-period interval. - $y=3+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)$ $Graph the function over a one-period interval. - y=3+\frac{1}{2} \cos 4\left(x+\frac{\pi}{2}\right)$

Solve the problem. -A spring with a spring constant of 5 and a 1-unit mass attached to it is stretched $3 \mathrm { ft }$ and released. What is the equation for the resulting oscillatory motion?