Question 1

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

Accepted Answer

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

Question 2

Graph the function over a one-period interval.
-The weekly sales in thousands of items of a product has a seasonal sales record approximated by $$\mathrm { n } = 59.02 + 21.5 \sin \frac { \pi \mathrm { t } } { 24 } ( \mathrm { t } = \text { time in weeks with } \mathrm { t } = 1 \text { referring to the first week in the year } ) \text {. During }$$ which week(s) will the sales equal 69,770 items?

Accepted Answer

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

Question 3

Find the corresponding angle measure in radians.
-$90 ^ { \circ }$

Accepted Answer

A)  $\frac { 5 \pi } { 6 }$ 
B)  $\frac { 11 \pi } { 6 }$ 
C)  $\frac { \pi } { 2 }$ 
D)  $\frac { 4 \pi } { 3 }$ 
A)  $\frac { 5 \pi } { 6 }$ 
B)  $\frac { 11 \pi } { 6 }$ 
C)  $\frac { \pi } { 2 }$ 
D)  $\frac { 4 \pi } { 3 }$

Question 4

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Us $$3.1416 \text { for } \pi$$
-$3.6057$

Accepted Answer

A)  $206.59 ^ { \circ }$ 
B)  $205.89 ^ { \circ }$ 
C)  $207.59 ^ { \circ }$ 
D)  $207.09 ^ { \circ }$ 
A)  $206.59 ^ { \circ }$ 
B)  $205.89 ^ { \circ }$ 
C)  $207.59 ^ { \circ }$ 
D)  $207.09 ^ { \circ }$

Question 5

Graph the function.
-$$y = - \frac { 1 } { 2 } \cos \left( x + \frac { \pi } { 4 } \right)$$

Accepted Answer

A) 
  
B)

C) 
  
D) 
  
A) 
  
B)

C) 
  
D)

Question 6

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-A pulley with a diameter of 28 inches is driven by a belt which is moving $1035 \mathrm { ft } / \mathrm { min }$. To the nearest unit, how many revolutions per minute are made by the pulley?

Accepted Answer

A)  $246 \mathrm { rpm }$ 
B)  $141 \mathrm { rpm }$ 
C)  $239 \mathrm { rpm }$ 
D)  $153 \mathrm { rpm }$ 
A)  $246 \mathrm { rpm }$ 
B)  $141 \mathrm { rpm }$ 
C)  $239 \mathrm { rpm }$ 
D)  $153 \mathrm { rpm }$

Question 7

Solve the problem
-A pulley of radius $11 \mathrm {~cm}$ rotates 15 times in $4 \mathrm { sec }$. Find the angular speed of the pulley.

Accepted Answer

A)  $\frac { 165 \pi } { 4 }$ radians per sec 
B)  $\frac { 2 \pi } { 165 }$ radian per $\mathrm { sec }$ 
C)  $\frac { 4 \pi } { 165 }$ radian per sec 
D)  $\frac { 15 \pi } { 2 }$ radians per sec 
A)  $\frac { 165 \pi } { 4 }$ radians per sec 
B)  $\frac { 2 \pi } { 165 }$ radian per $\mathrm { sec }$ 
C)  $\frac { 4 \pi } { 165 }$ radian per sec 
D)  $\frac { 15 \pi } { 2 }$ radians per sec

Question 8

Find the area of a sector of a circle having radius r and central angle $$\theta$$ . If necessary, express the answer to the nearest
tenth.
-$$\mathrm { r } = 15.0 \mathrm {~m} , \theta = 20 ^ { \circ }$$

Accepted Answer

A)  $39.3 \mathrm {~m} ^ { 2 }$ 
B)  $78.5 \mathrm {~m} ^ { 2 }$ 
C)  $2.6 \mathrm {~m} ^ { 2 }$ 
D)  $0.5 \mathrm {~m} ^ { 2 }$ 
A)  $39.3 \mathrm {~m} ^ { 2 }$ 
B)  $78.5 \mathrm {~m} ^ { 2 }$ 
C)  $2.6 \mathrm {~m} ^ { 2 }$ 
D)  $0.5 \mathrm {~m} ^ { 2 }$

Question 9

Find the exact value of s in the given interval that has the given circular function value.
-$$\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1$$

Accepted Answer

A)  $s = \frac { \pi } { 4 }$ 
B)  $s = \frac { 4 \pi } { 3 }$ 
C)  $s = \frac { 7 \pi } { 6 }$ 
D)  $s = \frac { 5 \pi } { 4 }$ 
A)  $s = \frac { \pi } { 4 }$ 
B)  $s = \frac { 4 \pi } { 3 }$ 
C)  $s = \frac { 7 \pi } { 6 }$ 
D)  $s = \frac { 5 \pi } { 4 }$

Question 10

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

Accepted Answer

A)  $\frac { 12 } { 5 }$ 
B)  $- \frac { 5 } { 12 }$ 
C)  $- \frac { 13 } { 12 }$ 
D)  $- \frac { 12 } { 5 }$ 
A)  $\frac { 12 } { 5 }$ 
B)  $- \frac { 5 } { 12 }$ 
C)  $- \frac { 13 } { 12 }$ 
D)  $- \frac { 12 } { 5 }$

Question 11

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated.
-$\theta = \frac { \pi } { 10 }$ radian, $t = 7 \mathrm { sec }$

Accepted Answer

A)  $\frac { \pi } { 70 }$ radian per sec 
B)  $\frac { 10 \pi } { 7 }$ radians per sec 
C)  $\frac { 70 } { \pi }$ radians per sec 
D)  $\frac { 7 \pi } { 10 }$ radians per sec 
A)  $\frac { \pi } { 70 }$ radian per sec 
B)  $\frac { 10 \pi } { 7 }$ radians per sec 
C)  $\frac { 70 } { \pi }$ radians per sec 
D)  $\frac { 7 \pi } { 10 }$ radians per sec

Question 12

Find the exact values of s in the given interval that satisfy the given condition.
-$[ 0,2 \pi ) ; \sin \mathrm { s } = \frac { \sqrt { 3 } } { 2 }$

Accepted Answer

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

Question 13

The function graphed is of the form y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$$ Determine the equation of the graph.
-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. When does the machine first reach its full power?

Accepted Answer

A)  After 4 hours 
B)  After 14 hours 
C)  After 2 hours 
D)  After 7 hours 
A)  After 4 hours 
B)  After 14 hours 
C)  After 2 hours 
D)  After 7 hours

Question 14

The function graphed is of the form y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$$ Determine the equation of the graph.
-For an electrical circuit, the voltage $\mathrm { E }$ is modeled by $\mathrm { E } = 2.7 \cos 28 \pi \mathrm { t }$, where $\mathrm { t }$ is the time in seconds. How many cycles are completed in one second?

Accepted Answer

A)  14 cycles 
B)  $2.7$ cycles 
C)  28 cycles 
D)  $28 \pi$ cycles 
A)  14 cycles 
B)  $2.7$ cycles 
C)  28 cycles 
D)  $28 \pi$ cycles

Question 15

Find the exact value of s in the given interval that has the given circular function value.
-$$\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \tan \mathrm { s } = - \frac { \sqrt { 3 } } { 3 }$$

Accepted Answer

A)  $s = \frac { 7 \pi } { 4 }$ 
B)  $s = \frac { 11 \pi } { 6 }$ 
C)  $s = \frac { \pi } { 6 }$ 
D)  $s = \frac { 5 \pi } { 3 }$ 
A)  $s = \frac { 7 \pi } { 4 }$ 
B)  $s = \frac { 11 \pi } { 6 }$ 
C)  $s = \frac { \pi } { 6 }$ 
D)  $s = \frac { 5 \pi } { 3 }$

Question 16

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

Accepted Answer

A) 
  
B)

C) 
  
D) 
  
A) 
  
B)

C) 
  
D)

Question 17

Convert the degree measure to radians, correct to four decimal places. $$3.1416 \text { for } \pi \text {. }$$
-$- 237 ^ { \circ } 20 ^ { \prime }$

Accepted Answer

A)  $- 4.1423$ 
B)  $- 4.1123$ 
C)  $- 4.1323$ 
D)  $- 4.1223$ 
A)  $- 4.1423$ 
B)  $- 4.1123$ 
C)  $- 4.1323$ 
D)  $- 4.1223$

Question 18

Find the value of s in the interval [ $[ 0 , \pi / 2 ]$ /2] that makes the statement true. Round to four decimal places.
-$\cot \mathrm { s } = 8.3683$

Accepted Answer

A)  0.1189 
B)  1.1643 
C)  1.5935 
D)  3.2605 
A)  0.1189 
B)  1.1643 
C)  1.5935 
D)  3.2605

Question 19

The function graphed is of the form y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$$ Determine the equation of the graph.
-

Accepted Answer

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

Question 20

Determine the equation of the graph.
-A rotating beacon is located $13 \mathrm { ft }$ from a wall. The distance from the beacon to the point on the wall where the beacon is aimed is given by
$$a = 13 | \sec 2 \pi t | \text {, }$$
where $t$ is time measured in seconds since the beacon started rotating. Find a for $t = 0.41$ seconds. Ro your answer to the nearest hundredth.

Accepted Answer

A)  $15.40 \mathrm { ft }$ 
B)  $31.00 \mathrm { ft }$ 
C)  $46.60 \mathrm { ft }$ 
D)  $- 15.40 \mathrm { ft }$ nd 
A)  $15.40 \mathrm { ft }$ 
B)  $31.00 \mathrm { ft }$ 
C)  $46.60 \mathrm { ft }$ 
D)  $- 15.40 \mathrm { ft }$ nd

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

Find the corresponding angle measure in radians. - $90 ^ { \circ }$ $Find the corresponding angle measure in radians. - 90 ^ { \circ }$

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Us $3.1416 \text { for } \pi$ - $3.6057$

Graph the function. - $y = - \frac { 1 } { 2 } \cos \left( x + \frac { \pi } { 4 } \right)$ $Graph the function. - y = - \frac { 1 } { 2 } \cos \left( x + \frac { \pi } { 4 } \right)$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -A pulley with a diameter of 28 inches is driven by a belt which is moving $1035 \mathrm { ft } / \mathrm { min }$ . To the nearest unit, how many revolutions per minute are made by the pulley?

Solve the problem -A pulley of radius $11 \mathrm {~cm}$ rotates 15 times in $4 \mathrm { sec }$ . Find the angular speed of the pulley.

Find the area of a sector of a circle having radius r and central angle $\theta$ . If necessary, express the answer to the nearest tenth. - $\mathrm { r } = 15.0 \mathrm {~m} , \theta = 20 ^ { \circ }$

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1$

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\theta = \frac { \pi } { 10 }$ radian, $t = 7 \mathrm { sec }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \sin \mathrm { s } = \frac { \sqrt { 3 } } { 2 }$

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \tan \mathrm { s } = - \frac { \sqrt { 3 } } { 3 }$

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

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $- 237 ^ { \circ } 20 ^ { \prime }$

Find the value of s in the interval [ $[ 0 , \pi / 2 ]$ /2] that makes the statement true. Round to four decimal places. - $\cot \mathrm { s } = 8.3683$

The function graphed is of the form y $y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$ Determine the equation of the graph. - $The function graphed is of the form y y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0 Determine the equation of the graph. -$

Review of Basic Concepts

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

Filters

Exam 7: The Circular Functions and Their Graphs

Graph the function. - y=−2+cot⁡xy = - 2 + \cot xy=−2+cotx

Find the corresponding angle measure in radians. - 90∘90 ^ { \circ }90∘

Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Us 3.1416 for π3.1416 \text { for } \pi3.1416 for π - 3.60573.60573.6057

Graph the function. - y=−12cos⁡(x+π4)y = - \frac { 1 } { 2 } \cos \left( x + \frac { \pi } { 4 } \right)y=−21​cos(x+4π​)

Solve the problem -A pulley of radius 11 cm11 \mathrm {~cm}11 cm rotates 15 times in 4sec4 \mathrm { sec }4sec . Find the angular speed of the pulley.

Find the area of a sector of a circle having radius r and central angle θ\thetaθ . If necessary, express the answer to the nearest tenth. - r=15.0 m,θ=20∘\mathrm { r } = 15.0 \mathrm {~m} , \theta = 20 ^ { \circ }r=15.0 m,θ=20∘

Find the exact value of s in the given interval that has the given circular function value. - [π,3π2];tan⁡s=1\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1[π,23π​];tans=1

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

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. - θ=π10\theta = \frac { \pi } { 10 }θ=10π​ radian, t=7sect = 7 \mathrm { sec }t=7sec

Find the exact values of s in the given interval that satisfy the given condition. - [0,2π);sin⁡s=32[ 0,2 \pi ) ; \sin \mathrm { s } = \frac { \sqrt { 3 } } { 2 }[0,2π);sins=23​​

Find the exact value of s in the given interval that has the given circular function value. - [3π2,2π];tan⁡s=−33\left[ \frac { 3 \pi } { 2 } , 2 \pi \right] ; \tan \mathrm { s } = - \frac { \sqrt { 3 } } { 3 }[23π​,2π];tans=−33​​

Graph the function over a one-period interval. - y=14cos⁡2(x+π4)y = \frac { 1 } { 4 } \cos 2 \left( x + \frac { \pi } { 4 } \right)y=41​cos2(x+4π​)

Convert the degree measure to radians, correct to four decimal places. 3.1416 for π. 3.1416 \text { for } \pi \text {. }3.1416 for π. - −237∘20′- 237 ^ { \circ } 20 ^ { \prime }−237∘20′

Find the value of s in the interval [ [0,π/2][ 0 , \pi / 2 ][0,π/2] /2] that makes the statement true. Round to four decimal places. - cot⁡s=8.3683\cot \mathrm { s } = 8.3683cots=8.3683

The function graphed is of the form y y=asin⁡bx or y=acos⁡bx, where b>0y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0y=asinbx or y=acosbx, where b>0 Determine the equation of the graph. -