Question 1

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

Accepted Answer

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

Question 2

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places.
-$\cos s = 0.3889$

Accepted Answer

A)  $5.1118$ 
B)  $1.1714$ 
C)  $0.3994$ 
D)  $1.3130$ 
A)  $5.1118$ 
B)  $1.1714$ 
C)  $0.3994$ 
D)  $1.3130$

Question 3

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

Question 4

Solve the problem.
-A pendulum swings through an angle of $6 ^ { \circ }$ each second. If the pendulum is $19 \mathrm {~cm}$ in length and the complete swing from right to left lasts 3 seconds, what area is covered by each complete swing? Round to the nearest hundredth.

Accepted Answer

A)  $113.41 \mathrm {~cm} ^ { 2 }$ 
B)  $18.90 \mathrm {~cm} ^ { 2 }$ 
C)  $2.98 \mathrm {~cm} ^ { 2 }$ 
D)  $56.71 \mathrm {~cm} ^ { 2 }$ 
A)  $113.41 \mathrm {~cm} ^ { 2 }$ 
B)  $18.90 \mathrm {~cm} ^ { 2 }$ 
C)  $2.98 \mathrm {~cm} ^ { 2 }$ 
D)  $56.71 \mathrm {~cm} ^ { 2 }$

Question 5

Find the length of an arc intercepted by a central angle θin a circle of radius r. Round your answer to 1 decimal place.
-$r = 57.01$ in.; $\theta = 117 ^ { \circ }$

Accepted Answer

A)  $58.2 \mathrm { in }$. 
B)  $116.4 \mathrm { in }$. 
C)  $37.1 \mathrm { in } .$ 
D)  $232.8 \mathrm { in }$. 
A)  $58.2 \mathrm { in }$. 
B)  $116.4 \mathrm { in }$. 
C)  $37.1 \mathrm { in } .$ 
D)  $232.8 \mathrm { in }$.

Question 6

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
-$17.15 ^ { \circ }$

Accepted Answer

A)  $0.0993$ 
B)  $0.2993$ 
C)  $0.1993$ 
D)  $0.3993$ 
A)  $0.0993$ 
B)  $0.2993$ 
C)  $0.1993$ 
D)  $0.3993$

Question 7

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

Accepted Answer

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

Question 8

Solve the problem.
-The weekly sales in thousands of items of a product has a seasonal sales record approximated by $\mathrm { n } = 85.94 + 25.1 \sin \frac { \pi \mathrm { t } } { 24 } ( \mathrm { t } =$ time in weeks with $\mathrm { t } = 1$ referring to the first week in the year). During which week(s) will the sales equal 98,490 items?

Accepted Answer

A)  week 30 and week 47 
B)  week 4 and week 47 
C)  week 21 and week 30 
D)  week 4 , week 20 , and week 52 
A)  week 30 and week 47 
B)  week 4 and week 47 
C)  week 21 and week 30 
D)  week 4 , week 20 , and week 52

Question 9

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
-$$- \frac { 7 \pi } { 2 }$$

Accepted Answer

A)  $- 631 ^ { \circ }$ 
B)  $- 630.5 ^ { \circ }$ 
C)  $- 629.5 ^ { \circ }$ 
D)  $- 630 ^ { \circ }$ 
A)  $- 631 ^ { \circ }$ 
B)  $- 630.5 ^ { \circ }$ 
C)  $- 629.5 ^ { \circ }$ 
D)  $- 630 ^ { \circ }$

Question 10

Solve the problem.
-The radius of the tires of a car is 16 inches, and they are revolving at the rate of 691 revolutions per minute. How fast is the car traveling in miles per hour?

Accepted Answer

A)  $\frac { 691 } { 330 } \pi \mathrm { mph }$ 
B)  $\frac { 691 } { 33 } \pi \mathrm { mph }$ 
C)  $\frac { 691 } { 66 } \pi \mathrm { mph }$ 
D)  $\frac { 2764 } { 11 } \pi \mathrm { mph }$ 
A)  $\frac { 691 } { 330 } \pi \mathrm { mph }$ 
B)  $\frac { 691 } { 33 } \pi \mathrm { mph }$ 
C)  $\frac { 691 } { 66 } \pi \mathrm { mph }$ 
D)  $\frac { 2764 } { 11 } \pi \mathrm { mph }$

Question 11

Give the amplitude or period as requested.
-Period of $y = \cos 5 x$

Accepted Answer

A)  $\frac { 2 \pi } { 5 }$ 
B)  $2 \pi$ 
C)  1 
D)  5 
A)  $\frac { 2 \pi } { 5 }$ 
B)  $2 \pi$ 
C)  1 
D)  5

Question 12

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the
indicated circular function value of θ.
-Find $\cot \theta$.

Accepted Answer

A)  $- \frac { 24 } { 7 }$ 
B)  $- \frac { 7 } { 24 }$ 
C)  $\frac { 7 } { 24 }$ 
D)  $\frac { 24 } { 7 }$ 
A)  $- \frac { 24 } { 7 }$ 
B)  $- \frac { 7 } { 24 }$ 
C)  $\frac { 7 } { 24 }$ 
D)  $\frac { 24 } { 7 }$

Question 13

Give the amplitude or period as requested.
-Period of $y = \sin 3 x$

Accepted Answer

A)  1 
B)  3 
C)  $2 \pi$ 
D)  $\frac { 2 \pi } { 3 }$ 
A)  1 
B)  3 
C)  $2 \pi$ 
D)  $\frac { 2 \pi } { 3 }$

Question 14

Solve the problem.
-The position of a weight attached to a spring is $s ( t ) = - 8 \cos 8 \pi t$ inches after $t$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height? Round values to two decimal places, if necessary.

Accepted Answer

A)  The maximum height of 16 inches is first reached after 2 seconds. 
B)  The maximum height of 8 inches is first reached after $0.13$ seconds. 
C)  The maximum height of 16 inches is first reached after 4 seconds. 
D)  The maximum height of 8 inches is first reached after 4 seconds. 
A)  The maximum height of 16 inches is first reached after 2 seconds. 
B)  The maximum height of 8 inches is first reached after $0.13$ seconds. 
C)  The maximum height of 16 inches is first reached after 4 seconds. 
D)  The maximum height of 8 inches is first reached after 4 seconds.

Question 15

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

Accepted Answer

A)  $y = 5 \cos \left( \frac { 1 } { 2 } x \right)$ 
B)  $y = - 5 \cos ( 2 x )$ 
C)  $y = 5 \sin ( 2 x )$ 
D)  $y = - 5 \cos \left( \frac { 1 } { 2 } x \right)$ 
A)  $y = 5 \cos \left( \frac { 1 } { 2 } x \right)$ 
B)  $y = - 5 \cos ( 2 x )$ 
C)  $y = 5 \sin ( 2 x )$ 
D)  $y = - 5 \cos \left( \frac { 1 } { 2 } x \right)$

Question 16

Graph the function.
-$y=\frac{4}{3} \cos \frac{1}{2} x$

Accepted Answer

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

Question 17

Give the amplitude or period as requested.
-Amplitude of $y = - 2 \sin 3 x$

Accepted Answer

A)  2 
B)  $\frac { \pi } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { \pi } { 2 }$ 
A)  2 
B)  $\frac { \pi } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { \pi } { 2 }$

Question 18

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
-$\frac { 5 \pi } { 2 }$

Accepted Answer

A)  $72 \pi ^ { \circ }$ 
B)  $144 ^ { \circ }$ 
C)  $900 ^ { \circ }$ 
D)  $450 ^ { \circ }$ 
A)  $72 \pi ^ { \circ }$ 
B)  $144 ^ { \circ }$ 
C)  $900 ^ { \circ }$ 
D)  $450 ^ { \circ }$

Question 19

Graph the function.
-$$\begin{array}{l}
y = \csc \left( \frac { 2 } { 3 } x - \frac { \pi } { 6 } \right)\

\end{array}$$

Accepted Answer

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

Question 20

Graph the function.
-$y=2 \tan x$

Accepted Answer

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

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

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - $\cos s = 0.3889$

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. -

Solve the problem. -A pendulum swings through an angle of $6 ^ { \circ }$ each second. If the pendulum is $19 \mathrm {~cm}$ in length and the complete swing from right to left lasts 3 seconds, what area is covered by each complete swing? Round to the nearest hundredth.

Find the length of an arc intercepted by a central angle θin a circle of radius r. Round your answer to 1 decimal place. - $r = 57.01$ in.; $\theta = 117 ^ { \circ }$

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $17.15 ^ { \circ }$

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

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { 7 \pi } { 2 }$

Solve the problem. -The radius of the tires of a car is 16 inches, and they are revolving at the rate of 691 revolutions per minute. How fast is the car traveling in miles per hour?

Give the amplitude or period as requested. -Period of $y = \cos 5 x$

Give the amplitude or period as requested. -Period of $y = \sin 3 x$

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

Graph the function. - $y=\frac{4}{3} \cos \frac{1}{2} x$ $Graph the function. - y=\frac{4}{3} \cos \frac{1}{2} x$

Give the amplitude or period as requested. -Amplitude of $y = - 2 \sin 3 x$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 5 \pi } { 2 }$

Graph the function. - y= x- $Graph the function. - \begin{array}{l} y = \csc \left( \frac { 2 } { 3 } x - \frac { \pi } { 6 } \right)\\ \end{array}$

Graph the function. - $y=2 \tan x$ $Graph the function. - y=2 \tan x$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 6: The Circular Functions and Their Graphs

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

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - cos⁡s=0.3889\cos s = 0.3889coss=0.3889

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. -

Solve the problem. -A pendulum swings through an angle of 6∘6 ^ { \circ }6∘ each second. If the pendulum is 19 cm19 \mathrm {~cm}19 cm in length and the complete swing from right to left lasts 3 seconds, what area is covered by each complete swing? Round to the nearest hundredth.

Find the length of an arc intercepted by a central angle θin a circle of radius r. Round your answer to 1 decimal place. - r=57.01r = 57.01r=57.01 in.; θ=117∘\theta = 117 ^ { \circ }θ=117∘

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - 17.15∘17.15 ^ { \circ }17.15∘

Graph the function over a one-period interval. - y=12sin⁡(x+π)y = \frac { 1 } { 2 } \sin ( x + \pi )y=21​sin(x+π)

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - −7π2- \frac { 7 \pi } { 2 }−27π​

Solve the problem. -The radius of the tires of a car is 16 inches, and they are revolving at the rate of 691 revolutions per minute. How fast is the car traveling in miles per hour?

Give the amplitude or period as requested. -Period of y=cos⁡5xy = \cos 5 xy=cos5x

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find cot⁡θ\cot \thetacotθ .

Give the amplitude or period as requested. -Period of y=sin⁡3xy = \sin 3 xy=sin3x

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

Graph the function. - y=43cos⁡12xy=\frac{4}{3} \cos \frac{1}{2} xy=34​cos21​x

Give the amplitude or period as requested. -Amplitude of y=−2sin⁡3xy = - 2 \sin 3 xy=−2sin3x

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - 5π2\frac { 5 \pi } { 2 }25π​

Graph the function. - y= x-

Graph the function. - y=2tan⁡xy=2 \tan xy=2tanx

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

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

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - $\cos s = 0.3889$

Solve the problem. -A pendulum swings through an angle of $6 ^ { \circ }$ each second. If the pendulum is $19 \mathrm {~cm}$ in length and the complete swing from right to left lasts 3 seconds, what area is covered by each complete swing? Round to the nearest hundredth.

Find the length of an arc intercepted by a central angle θin a circle of radius r. Round your answer to 1 decimal place. - $r = 57.01$ in.; $\theta = 117 ^ { \circ }$

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $17.15 ^ { \circ }$

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

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { 7 \pi } { 2 }$

Give the amplitude or period as requested. -Period of $y = \cos 5 x$

Give the amplitude or period as requested. -Period of $y = \sin 3 x$

Graph the function. - $y=\frac{4}{3} \cos \frac{1}{2} x$ $Graph the function. - y=\frac{4}{3} \cos \frac{1}{2} x$

Give the amplitude or period as requested. -Amplitude of $y = - 2 \sin 3 x$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 5 \pi } { 2 }$

Graph the function. - y= x- $Graph the function. - \begin{array}{l} y = \csc \left( \frac { 2 } { 3 } x - \frac { \pi } { 6 } \right)\\ \end{array}$

Graph the function. - $y=2 \tan x$ $Graph the function. - y=2 \tan x$