Question 1

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

Accepted Answer

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

Question 2

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places.
-$\tan \mathrm { s } = 4.5653$

Accepted Answer

A)  $0.9280$ 
B)  $1.3552$ 
C)  $0.9260$ 
D)  $4.4968$ 
A)  $0.9280$ 
B)  $1.3552$ 
C)  $0.9260$ 
D)  $4.4968$ B

Question 3

Solve the problem.
-Let angle POQ be designated $\theta$. Angles $P Q R$ and VRQ are right angles. If $\theta = 31 ^ { \circ }$, find the length of US accurate to four decimal places.

Accepted Answer

A)  $1.6643$ 
B)  $0.5150$ 
C)  $0.6009$ 
D)  $1.1666$ 
A)  $1.6643$ 
B)  $0.5150$ 
C)  $0.6009$ 
D)  $1.1666$ A

Question 4

Find the corresponding angle measure in radians.
-$315 ^ { \circ }$

Accepted Answer

A)  $\frac { 2 \pi } { 3 }$ 
B)  $\frac { 5 \pi } { 4 }$ 
C)  $\frac { 3 \pi } { 4 }$ 
D)  $\frac { 7 \pi } { 4 }$ 
A)  $\frac { 2 \pi } { 3 }$ 
B)  $\frac { 5 \pi } { 4 }$ 
C)  $\frac { 3 \pi } { 4 }$ 
D)  $\frac { 7 \pi } { 4 }$

Question 5

Solve the problem.
-The chart represents the amount of fuel consumed by a machine used in manufacturing. The machine is turned on at the beginning of the day, takes a certain amount of time to reach its full power (the point at which it uses the most fuel per hour), runs for a certain number of hours, and is shut off at the end of the work day. The fuel usage per hour of the machine is represented by a periodic function. What is the period in hours of this function?

Accepted Answer

A)  Period $= 125$ hours 
B)  Period $= 7$ hours 
C)  Period $= 4$ hours 
D)  Period $= 14$ hours 
A)  Period $= 125$ hours 
B)  Period $= 7$ hours 
C)  Period $= 4$ hours 
D)  Period $= 14$ hours

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Solve the problem.
-The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 3.3 \cos 130 \pi \mathrm { t }$, where $t$ is time measured i seconds. Find the frequency of the function (that is, find the number of cycles or periods completed in one second).

Accepted Answer

A)  65 
B)  $\frac { 1 } { 130 }$ 
C)  130 
D)  $\frac { 1 } { 65 }$ 
A)  65 
B)  $\frac { 1 } { 130 }$ 
C)  130 
D)  $\frac { 1 } { 65 }$

Question 9

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

Accepted Answer

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

Question 10

Find the specified quantity.
-Find the vertical translation of $y = - 3 + 2 \sin \left( 4 x + \frac { \pi } { 2 } \right)$.

Accepted Answer

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

Question 11

Match the function with its graph.
-1) $\mathrm { y } = \tan \mathrm { x }$
2) $\mathrm { y } = \cot \mathrm { x }$
3) $y = - \tan x$
4) $y = - \cot x$

A.
 
B.
 
C.
 
D.

Accepted Answer

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

Question 12

Find the exact circular function value.
-$$\csc \frac { - 2 \pi } { 3 }$$

Accepted Answer

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

Question 13

Find the phase shift of the function.
-$$y = \sin \left( x + \frac { \pi } { 4 } \right)$$

Accepted Answer

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

Question 14

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

A.
 
B.
 
C.
 
D.

Accepted Answer

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

Question 15

Solve the problem.
-The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 1.9 \cos 140 \pi \mathrm { t }$, where $\mathrm { t }$ is time measured in seconds. Find the period.

Accepted Answer

A)  $70 \pi$ 
B)  70 
C)  $\frac { 1 } { 70 }$ 
D)  $\frac { \pi } { 70 }$ 
A)  $70 \pi$ 
B)  70 
C)  $\frac { 1 } { 70 }$ 
D)  $\frac { \pi } { 70 }$

Question 16

Find the specified quantity.
-Find the amplitude of $y = 5 \sin \left( 4 x + \frac { \pi } { 4 } \right)$.

Accepted Answer

A)  4 
B)  $\frac { \pi } { 4 }$ 
C)  20 
D)  5 
A)  4 
B)  $\frac { \pi } { 4 }$ 
C)  20 
D)  5

Question 17

Determine the equation of the graph.
-

Accepted Answer

A)  $y = \csc 4 x$ 
B)  $y = 4 \csc x$ 
C)  $y = 4 \sec x$ 
D)  $y = \sec 4 x$ 
A)  $y = \csc 4 x$ 
B)  $y = 4 \csc x$ 
C)  $y = 4 \sec x$ 
D)  $y = \sec 4 x$

Question 18

Solve the problem.
-Tides go up and down in a 14.8-hour period. The average depth of a certain river is $13 \mathrm {~m}$ and ranges from 8 to $18 \mathrm {~m}$. The variation can be approximated by a sine curve. Write an equation that gives the approximate variation $y$, if $x$ is the number of hours after midnight and high tide occurs at 10:00 am.

Accepted Answer

A)  $y = 13 \sin \left( \frac { \pi x } { 7.4 } - \frac { 10 \pi } { 7.4 } \right)$ 
B)  $\mathrm { y } = 13 \sin \left( \frac { \pi \mathrm { x } } { 7.4 } - 10 \pi \right)$ 
C)  $\mathrm { y } = 5 \sin \left( \frac { \pi \mathrm { x } } { 7.4 } - \frac { 10 \pi } { 7.4 } \right)$ 
D)  $y = 5 \sin \left( \frac { \pi x } { 7.4 } - \frac { 6.3 \pi } { 7.4 } \right)$ 
A)  $y = 13 \sin \left( \frac { \pi x } { 7.4 } - \frac { 10 \pi } { 7.4 } \right)$ 
B)  $\mathrm { y } = 13 \sin \left( \frac { \pi \mathrm { x } } { 7.4 } - 10 \pi \right)$ 
C)  $\mathrm { y } = 5 \sin \left( \frac { \pi \mathrm { x } } { 7.4 } - \frac { 10 \pi } { 7.4 } \right)$ 
D)  $y = 5 \sin \left( \frac { \pi x } { 7.4 } - \frac { 6.3 \pi } { 7.4 } \right)$

Question 19

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 20

Graph the function.
-$y=\frac{6}{5} \sec \left(\frac{5}{4} x-\frac{\pi}{5}\right)$

Accepted Answer

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

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

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - $\tan \mathrm { s } = 4.5653$

Find the corresponding angle measure in radians. - $315 ^ { \circ }$ $Find the corresponding angle measure in radians. - 315 ^ { \circ }$

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

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

Solve the problem. -The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 3.3 \cos 130 \pi \mathrm { t }$ , where $t$ is time measured i seconds. Find the frequency of the function (that is, find the number of cycles or periods completed in one second).

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

Find the specified quantity. -Find the vertical translation of $y = - 3 + 2 \sin \left( 4 x + \frac { \pi } { 2 } \right)$ .

Find the exact circular function value. - $\csc \frac { - 2 \pi } { 3 }$

Find the phase shift of the function. - $y = \sin \left( x + \frac { \pi } { 4 } \right)$

Solve the problem. -The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 1.9 \cos 140 \pi \mathrm { t }$ , where $\mathrm { t }$ is time measured in seconds. Find the period.

Find the specified quantity. -Find the amplitude of $y = 5 \sin \left( 4 x + \frac { \pi } { 4 } \right)$ .

Determine the equation of the graph. -

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. - $y=\frac{6}{5} \sec \left(\frac{5}{4} x-\frac{\pi}{5}\right)$ $Graph the function. - y=\frac{6}{5} \sec \left(\frac{5}{4} x-\frac{\pi}{5}\right)$

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

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Exam 6: The Circular Functions and Their Graphs

Graph the function. - y=−cos⁡πxy=-\cos \pi xy=−cosπx

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - tan⁡s=4.5653\tan \mathrm { s } = 4.5653tans=4.5653

Solve the problem. -Let angle POQ be designated θ\thetaθ . Angles PQRP Q RPQR and VRQ are right angles. If θ=31∘\theta = 31 ^ { \circ }θ=31∘ , find the length of US accurate to four decimal places.

Find the corresponding angle measure in radians. - 315∘315 ^ { \circ }315∘

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

Graph the function. - y=14tan⁡2xy = \frac { 1 } { 4 } \tan 2 xy=41​tan2x

Graph the function. - y=−2sin⁡xy=-2 \sin xy=−2sinx

Find the specified quantity. -Find the vertical translation of y=−3+2sin⁡(4x+π2)y = - 3 + 2 \sin \left( 4 x + \frac { \pi } { 2 } \right)y=−3+2sin(4x+2π​) .

Match the function with its graph. -1) y=tan⁡x\mathrm { y } = \tan \mathrm { x }y=tanx 2) y=cot⁡x\mathrm { y } = \cot \mathrm { x }y=cotx 3) y=−tan⁡xy = - \tan xy=−tanx 4) y=−cot⁡xy = - \cot xy=−cotx A. B. C. D.

Find the exact circular function value. - csc⁡−2π3\csc \frac { - 2 \pi } { 3 }csc3−2π​

Find the phase shift of the function. - y=sin⁡(x+π4)y = \sin \left( x + \frac { \pi } { 4 } \right)y=sin(x+4π​)

Match the function with its graph. -1) y=sin⁡13xy = \sin \frac { 1 } { 3 } xy=sin31​x 2) y=13cos⁡xy = \frac { 1 } { 3 } \cos xy=31​cosx 3) y=13sin⁡xy = \frac { 1 } { 3 } \sin xy=31​sinx 4) y=cos⁡13xy = \cos \frac { 1 } { 3 } xy=cos31​x A. B. C. D.

Solve the problem. -The voltage E\mathrm { E }E in an electrical circuit is given by E=1.9cos⁡140πt\mathrm { E } = 1.9 \cos 140 \pi \mathrm { t }E=1.9cos140πt , where t\mathrm { t }t is time measured in seconds. Find the period.

Find the specified quantity. -Find the amplitude of y=5sin⁡(4x+π4)y = 5 \sin \left( 4 x + \frac { \pi } { 4 } \right)y=5sin(4x+4π​) .

Determine the equation of the graph. -

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=65sec⁡(54x−π5)y=\frac{6}{5} \sec \left(\frac{5}{4} x-\frac{\pi}{5}\right)y=56​sec(45​x−5π​)

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

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - $\tan \mathrm { s } = 4.5653$

Find the corresponding angle measure in radians. - $315 ^ { \circ }$ $Find the corresponding angle measure in radians. - 315 ^ { \circ }$

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

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

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

Find the specified quantity. -Find the vertical translation of $y = - 3 + 2 \sin \left( 4 x + \frac { \pi } { 2 } \right)$ .

Find the exact circular function value. - $\csc \frac { - 2 \pi } { 3 }$

Find the phase shift of the function. - $y = \sin \left( x + \frac { \pi } { 4 } \right)$

Solve the problem. -The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 1.9 \cos 140 \pi \mathrm { t }$ , where $\mathrm { t }$ is time measured in seconds. Find the period.

Find the specified quantity. -Find the amplitude of $y = 5 \sin \left( 4 x + \frac { \pi } { 4 } \right)$ .

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. - $y=\frac{6}{5} \sec \left(\frac{5}{4} x-\frac{\pi}{5}\right)$ $Graph the function. - y=\frac{6}{5} \sec \left(\frac{5}{4} x-\frac{\pi}{5}\right)$