Question 1

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)  $y = 5 \sin \left( \frac { 1 } { 3 } x \right)$ 
B)  $y = - 5 \cos ( 3 x )$ 
C)  $y = 5 \cos ( 3 x )$ 
D)  $y = 5 \cos \left( \frac { 1 } { 3 } x \right)$ 
A)  $y = 5 \sin \left( \frac { 1 } { 3 } x \right)$ 
B)  $y = - 5 \cos ( 3 x )$ 
C)  $y = 5 \cos ( 3 x )$ 
D)  $y = 5 \cos \left( \frac { 1 } { 3 } x \right)$

Question 2

Use a table or a calculator to evaluate the function. Round to four decimal places.
-sec $0.2451$

Accepted Answer

A)  $0.9701$ 
B)  $0.2501$ 
C)  $1.0308$ 
D)  $0.2427$ 
A)  $0.9701$ 
B)  $0.2501$ 
C)  $1.0308$ 
D)  $0.2427$

Question 3

Graph the function.
-$y=\sin \frac{2}{3} x$

Accepted Answer

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

Question 4

Find the specified quantity.
-Find the period of $y = - 3 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 3 } \right)$.

Accepted Answer

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

Question 5

Determine the equation of the graph.
-

Accepted Answer

A)  $y = \csc 2 x$ 
B)  $y = 2 \sec x$ 
C)  $y = \sec 2 x$ 
D)  $y = 2 \csc x$ 
A)  $y = \csc 2 x$ 
B)  $y = 2 \sec x$ 
C)  $y = \sec 2 x$ 
D)  $y = 2 \csc x$

Question 6

Use a table or a calculator to evaluate the function. Round to four decimal places.
-$\tan 0.2220$

Accepted Answer

A)  $0.2202$ 
B)  $0.2257$ 
C)  $1.0252$ 
D)  $0.9755$ 
A)  $0.2202$ 
B)  $0.2257$ 
C)  $1.0252$ 
D)  $0.9755$

Question 7

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

Accepted Answer

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

Question 8

Match the function with its graph.
-1) $y = - \csc x$
2) $y = - \sec x$
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)  $1 \mathrm { C } , 2 \mathrm {~A} , 3 \mathrm {~B} , 4 \mathrm { D }$ 
C)  $1 \mathrm {~A} , 2 \mathrm {~B} , 3 \mathrm { C } , 4 \mathrm { D }$ 
D)  $1 \mathrm {~B} , 2 \mathrm { D } , 3 \mathrm { C } , 4 \mathrm {~A}$ 
A)  $1 \mathrm {~A} , 2 \mathrm { D } , 3 \mathrm { C } , 4 \mathrm {~B}$ 
B)  $1 \mathrm { C } , 2 \mathrm {~A} , 3 \mathrm {~B} , 4 \mathrm { D }$ 
C)  $1 \mathrm {~A} , 2 \mathrm {~B} , 3 \mathrm { C } , 4 \mathrm { D }$ 
D)  $1 \mathrm {~B} , 2 \mathrm { D } , 3 \mathrm { C } , 4 \mathrm {~A}$

Question 9

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)  $y = 2 \cos \left( \frac { 1 } { 3 } x \right)$ 
B)  $y = - 2 \cos ( 3 x )$ 
C)  $y = 2 \sin ( 3 x )$ 
D)  $y = - 2 \sin ( 3 x )$ 
A)  $y = 2 \cos \left( \frac { 1 } { 3 } x \right)$ 
B)  $y = - 2 \cos ( 3 x )$ 
C)  $y = 2 \sin ( 3 x )$ 
D)  $y = - 2 \sin ( 3 x )$

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)  $y = \sin x - 4$ 
B)  $y = \cos x - 4$ 
C)  $y = \cos ( x + 4 )$ 
D)  $y = \sin ( x - 4 )$ 
A)  $y = \sin x - 4$ 
B)  $y = \cos x - 4$ 
C)  $y = \cos ( x + 4 )$ 
D)  $y = \sin ( x - 4 )$

Question 11

Use the formula $$\omega = \frac { \theta } { t }$$ to find the value of the missing variable. Give an exact answer unless otherwise indicated.
-$\omega = \frac { \pi } { 2 }$ radian per $\mathrm { min } , \mathrm { t } = 5 \mathrm {~min}$

Accepted Answer

A)  $\frac { \pi } { 10 }$ radian 
B)  $\frac { 5 \pi } { 2 }$ radians 
C)  $\frac { 2 \pi } { 5 }$ radians 
D)  $\frac { 10 } { \pi }$ radians 
A)  $\frac { \pi } { 10 }$ radian 
B)  $\frac { 5 \pi } { 2 }$ radians 
C)  $\frac { 2 \pi } { 5 }$ radians 
D)  $\frac { 10 } { \pi }$ radians

Question 12

Solve the problem.
-A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 4 }$ second, determine a trigonometric model that gives the position of the weight at time $\mathrm { t }$ seconds.

Accepted Answer

A)  $\mathrm { y } = 5 \cos 8 \pi \mathrm { t }$ 
B)  $\mathrm { y } = - 5 \cos 8 \pi \mathrm { t }$ 
C)  $y = - 5 \cos 4 \pi t$ 
D)  $y = 5 \cos \frac { 1 } { 4 } t$ 
A)  $\mathrm { y } = 5 \cos 8 \pi \mathrm { t }$ 
B)  $\mathrm { y } = - 5 \cos 8 \pi \mathrm { t }$ 
C)  $y = - 5 \cos 4 \pi t$ 
D)  $y = 5 \cos \frac { 1 } { 4 } t$

Question 13

Use the formula $s = r \omega t$ to find the value of the missing variable. Give an exact answer.
-$\mathrm { r } = 16 \mathrm {~cm} , \omega = \frac { \pi } { 3 }$ radian per $\mathrm { sec } , \mathrm { t } = 16 \mathrm { sec }$

Accepted Answer

A)  $\frac { 256 } { 3 \pi } \mathrm { cm }$ 
B)  $\frac { 256 \pi } { 3 } \mathrm {~cm}$ 
C)  $\frac { 3 \pi } { 256 } \mathrm {~cm}$ 
D)  $\frac { 3 } { 256 \pi } \mathrm { cm }$ 
A)  $\frac { 256 } { 3 \pi } \mathrm { cm }$ 
B)  $\frac { 256 \pi } { 3 } \mathrm {~cm}$ 
C)  $\frac { 3 \pi } { 256 } \mathrm {~cm}$ 
D)  $\frac { 3 } { 256 \pi } \mathrm { cm }$

Question 14

Find the specified quantity.
-Find the period of $y = 5 \sin \left( \frac { 1 } { 2 } x - \frac { \pi } { 2 } \right)$.

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Solve the problem.
-The position of a weight attached to a spring is $s ( t ) = - 3 \cos 7 \pi t$ inches after $t$ seconds. When does the weight first reach its maximum height?

Accepted Answer

A)  After $\frac { \pi } { 7 } \mathrm { sec }$ 
B)  After $\frac { 1 } { 7 } \mathrm { sec }$ 
C)  After $\frac { 7 } { \pi } \mathrm { sec }$ 
D)  After $\frac { 7 } { 4 } \mathrm { sec }$ 
A)  After $\frac { \pi } { 7 } \mathrm { sec }$ 
B)  After $\frac { 1 } { 7 } \mathrm { sec }$ 
C)  After $\frac { 7 } { \pi } \mathrm { sec }$ 
D)  After $\frac { 7 } { 4 } \mathrm { sec }$

Question 17

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places.
-$\cot \mathrm { s } = 8.3122$

Accepted Answer

A)  $1.5927$ 
B)  $3.2613$ 
C)  $0.1197$ 
D)  $1.1635$ 
A)  $1.5927$ 
B)  $3.2613$ 
C)  $0.1197$ 
D)  $1.1635$

Question 18

Solve the problem.
-The path of a projectile fired at an inclination $\theta$ to the horizontal with an initial speed $v _ { O }$ is a parabola. The range $\mathrm { R }$ of the projectile, the horizontal distance that the projectile travels, is found by the formula $\mathrm { R } = \frac { \mathrm { v } _ { \mathrm { O } } ^ { 2 } \sin 2 \theta } { \mathrm { g } }$ where $\mathrm { g } = 32.2$ feet per second per second or $\mathrm { g } = 9.8$ meters per second per second. Find the range of a projectile fired with an initial velocity of 144 feet per second at an angle of $35 ^ { \circ }$ to the horizontal. Round your answer to two decimal places.

Accepted Answer

A)  $369.37 \mathrm { ft }$ 
B)  $738.74 \mathrm { ft }$ 
C)  $605.14 \mathrm { ft }$ 
D)  $605.04 \mathrm { ft }$ 
A)  $369.37 \mathrm { ft }$ 
B)  $738.74 \mathrm { ft }$ 
C)  $605.14 \mathrm { ft }$ 
D)  $605.04 \mathrm { ft }$

Question 19

Solve the problem.
-Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is $4.7$ centimeters and the radius of the larger wheel is $16.1$ centimeters. Through how many degrees (to the nearest hundredth of a degree) will the larger wheel rotate if the smaller one rotates $220 ^ { \circ }$ ?

Accepted Answer

A)  $64.22 ^ { \circ }$ 
B)  $66.22 ^ { \circ }$ 
C)  $64.12 ^ { \circ }$ 
D)  $65.22 ^ { \circ }$ 
A)  $64.22 ^ { \circ }$ 
B)  $66.22 ^ { \circ }$ 
C)  $64.12 ^ { \circ }$ 
D)  $65.22 ^ { \circ }$

Question 20

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

Accepted Answer

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

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. -

Use a table or a calculator to evaluate the function. Round to four decimal places. -sec $0.2451$

Graph the function. - $y=\sin \frac{2}{3} x$ $Graph the function. - y=\sin \frac{2}{3} x$

Find the specified quantity. -Find the period of $y = - 3 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 3 } \right)$ .

Determine the equation of the graph. -

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\tan 0.2220$

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

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. -

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. -

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\omega = \frac { \pi } { 2 }$ radian per $\mathrm { min } , \mathrm { t } = 5 \mathrm {~min}$

Solve the problem. -A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 4 }$ second, determine a trigonometric model that gives the position of the weight at time $\mathrm { t }$ seconds.

Use the formula $s = r \omega t$ to find the value of the missing variable. Give an exact answer. - $\mathrm { r } = 16 \mathrm {~cm} , \omega = \frac { \pi } { 3 }$ radian per $\mathrm { sec } , \mathrm { t } = 16 \mathrm { sec }$

Find the specified quantity. -Find the period of $y = 5 \sin \left( \frac { 1 } { 2 } x - \frac { \pi } { 2 } \right)$ .

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

Solve the problem. -The position of a weight attached to a spring is $s ( t ) = - 3 \cos 7 \pi t$ inches after $t$ seconds. When does the weight first reach its maximum height?

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - $\cot \mathrm { s } = 8.3122$

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

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

Filters

Exam 6: The Circular Functions and Their Graphs

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. -

Use a table or a calculator to evaluate the function. Round to four decimal places. -sec 0.24510.24510.2451

Graph the function. - y=sin⁡23xy=\sin \frac{2}{3} xy=sin32​x

Find the specified quantity. -Find the period of y=−3cos⁡(12x+π3)y = - 3 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 3 } \right)y=−3cos(21​x+3π​) .

Determine the equation of the graph. -

Use a table or a calculator to evaluate the function. Round to four decimal places. - tan⁡0.2220\tan 0.2220tan0.2220

Graph the function over a one-period interval. - y=2+13sin⁡(2x−π)y=2+\frac{1}{3} \sin (2 x-\pi)y=2+31​sin(2x−π)

Match the function with its graph. -1) y=−csc⁡xy = - \csc xy=−cscx 2) y=−sec⁡xy = - \sec xy=−secx 3) y=−tan⁡xy = - \tan xy=−tanx 4) y=−cot⁡xy = - \cot xy=−cotx A. B. C. D.

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. -

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. -

Use the formula ω=θt\omega = \frac { \theta } { t }ω=tθ​ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - ω=π2\omega = \frac { \pi } { 2 }ω=2π​ radian per min,t=5 min\mathrm { min } , \mathrm { t } = 5 \mathrm {~min}min,t=5 min

Solve the problem. -A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is 14\frac { 1 } { 4 }41​ second, determine a trigonometric model that gives the position of the weight at time t\mathrm { t }t seconds.

Use the formula s=rωts = r \omega ts=rωt to find the value of the missing variable. Give an exact answer. - r=16 cm,ω=π3\mathrm { r } = 16 \mathrm {~cm} , \omega = \frac { \pi } { 3 }r=16 cm,ω=3π​ radian per sec,t=16sec\mathrm { sec } , \mathrm { t } = 16 \mathrm { sec }sec,t=16sec

Find the specified quantity. -Find the period of y=5sin⁡(12x−π2)y = 5 \sin \left( \frac { 1 } { 2 } x - \frac { \pi } { 2 } \right)y=5sin(21​x−2π​) .

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

Solve the problem. -The position of a weight attached to a spring is s(t)=−3cos⁡7πts ( t ) = - 3 \cos 7 \pi ts(t)=−3cos7πt inches after ttt seconds. When does the weight first reach its maximum height?

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - cot⁡s=8.3122\cot \mathrm { s } = 8.3122cots=8.3122

Graph the function over a one-period interval. - y=12+cos⁡(2x−2π3)y=\frac{1}{2}+\cos \left(2 x-\frac{2 \pi}{3}\right)y=21​+cos(2x−32π​)

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

Use a table or a calculator to evaluate the function. Round to four decimal places. -sec $0.2451$

Graph the function. - $y=\sin \frac{2}{3} x$ $Graph the function. - y=\sin \frac{2}{3} x$

Find the specified quantity. -Find the period of $y = - 3 \cos \left( \frac { 1 } { 2 } x + \frac { \pi } { 3 } \right)$ .

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\tan 0.2220$

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

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\omega = \frac { \pi } { 2 }$ radian per $\mathrm { min } , \mathrm { t } = 5 \mathrm {~min}$

Solve the problem. -A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 4 }$ second, determine a trigonometric model that gives the position of the weight at time $\mathrm { t }$ seconds.

Use the formula $s = r \omega t$ to find the value of the missing variable. Give an exact answer. - $\mathrm { r } = 16 \mathrm {~cm} , \omega = \frac { \pi } { 3 }$ radian per $\mathrm { sec } , \mathrm { t } = 16 \mathrm { sec }$

Find the specified quantity. -Find the period of $y = 5 \sin \left( \frac { 1 } { 2 } x - \frac { \pi } { 2 } \right)$ .

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

Solve the problem. -The position of a weight attached to a spring is $s ( t ) = - 3 \cos 7 \pi t$ inches after $t$ seconds. When does the weight first reach its maximum height?

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - $\cot \mathrm { s } = 8.3122$

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