Question 1

Use a table or a calculator to evaluate the function. Round to four decimal places.
-$\csc 0.2756$

Accepted Answer

A)  $0.2721$ 
B)  $3.6748$ 
C)  $0.9623$ 
D)  $1.0392$ 
A)  $0.2721$ 
B)  $3.6748$ 
C)  $0.9623$ 
D)  $1.0392$

Question 2

Solve the problem.
-Find the radius (to the nearest hundredth of a millimeter) of a pulley if rotating the pulley $55.21 ^ { \circ }$ raises the pulley $17.5 \mathrm {~mm}$.

Accepted Answer

A)  $18.26 \mathrm {~mm}$ 
B)  $18.16 \mathrm {~mm}$ 
C)  $18.06 \mathrm {~mm}$ 
D)  $17.96 \mathrm {~mm}$ 
A)  $18.26 \mathrm {~mm}$ 
B)  $18.16 \mathrm {~mm}$ 
C)  $18.06 \mathrm {~mm}$ 
D)  $17.96 \mathrm {~mm}$

Question 3

Solve the problem.
-Let angle POQ be designated $\theta$. Angles $\mathrm { PQR }$ and VRQ are right angles. If $\theta = 38 ^ { \circ }$, find the length of PQ accurate to four decimal places.

Accepted Answer

A)  $0.6157$ 
B)  $0.7813$ 
C)  $0.7880$ 
D)  $1.6243$ 
A)  $0.6157$ 
B)  $0.7813$ 
C)  $0.7880$ 
D)  $1.6243$

Question 4

Solve the problem.
-Suppose that the average monthly low temperatures for a small town are shown in the table.
\begin{tabular} { l | l l l l l l l l l l l l } 
Month & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \
\hline Temperature $\left( { } ^ { \circ } \mathrm { F } \right)$ & 19 & 27 & 38 & 45 & 57 & 62 & 65 & 58 & 51 & 41 & 33 & 25
\end{tabular}
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)  $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 42$ 
D)  $f ( x ) = 42 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 23$ 
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)  $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 42$ 
D)  $f ( x ) = 42 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 23$

Question 5

Graph the function.
-$y=\frac{1}{3} \tan \left(\frac{4}{5} x+\frac{\pi}{5}\right)$

Accepted Answer

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

Question 6

Find the length of an arc intercepted by a central angle θin a circle of radius r. Round your answer to 1 decimal place.
-$\mathrm { r } = 10.63 \mathrm {~cm}$.; $\theta = \frac { 10 } { 9 } \pi$ radians

Accepted Answer

A)  $18.6 \mathrm {~cm}$ 
B)  $11.8 \mathrm {~cm}$ 
C)  $74.2 \mathrm {~cm}$ 
D)  $37.1 \mathrm {~cm}$ 
A)  $18.6 \mathrm {~cm}$ 
B)  $11.8 \mathrm {~cm}$ 
C)  $74.2 \mathrm {~cm}$ 
D)  $37.1 \mathrm {~cm}$

Question 7

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

Accepted Answer

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

Question 8

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, $43.15 ^ { \circ } \mathrm { N }$, are $486 \mathrm {~km}$ apart.

Accepted Answer

A)  $38.8 ^ { \circ } \mathrm { N }$ 
B)  $39.5 ^ { \circ } \mathrm { N }$ 
C)  $47.5 ^ { \circ } \mathrm { N }$ 
D)  $52.46 ^ { \circ } \mathrm { N }$ 
A)  $38.8 ^ { \circ } \mathrm { N }$ 
B)  $39.5 ^ { \circ } \mathrm { N }$ 
C)  $47.5 ^ { \circ } \mathrm { N }$ 
D)  $52.46 ^ { \circ } \mathrm { N }$

Question 9

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 $\sec \theta$.

Accepted Answer

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

Question 10

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
-$43 ^ { \circ }$

Accepted Answer

A)  $0.3752$ 
B)  $0.5003$ 
C)  $0.7505$ 
D)  $1.5010$ 
A)  $0.3752$ 
B)  $0.5003$ 
C)  $0.7505$ 
D)  $1.5010$

Question 11

Solve the problem.
-Find the radius of a circle in which a central angle of $\frac { \pi } { 3 }$ radian determines a sector of area 56 square meters. Round to the nearest hundredth.

Accepted Answer

A)  $10.34 \mathrm {~m}$ 
B)  $14.63 \mathrm {~m}$ 
C)  $7.31 \mathrm {~m}$ 
D)  $106.95 \mathrm {~m}$ 
A)  $10.34 \mathrm {~m}$ 
B)  $14.63 \mathrm {~m}$ 
C)  $7.31 \mathrm {~m}$ 
D)  $106.95 \mathrm {~m}$

Question 12

Use a table or a calculator to evaluate the function. Round to four decimal places.
-$\cot 0.1369$

Accepted Answer

A)  $7.2589$ 
B)  $1.0094$ 
C)  $0.1378$ 
D)  $0.9906$ 
A)  $7.2589$ 
B)  $1.0094$ 
C)  $0.1378$ 
D)  $0.9906$

Question 13

Graph the function over a one-period interval.
-$y=4+2 \sin (x-\pi)$

Accepted Answer

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

Question 14

Find the area of a sector of a circle having radius r and central angle θ. If necessary, express the answer to the nearest
tenth.
-$\mathrm { r } = 24.0 \mathrm { ft } , \theta = \frac { 2 \pi } { 3 }$ radians

Accepted Answer

A)  $52.6 \mathrm { ft } ^ { 2 }$ 
B)  $603.2 \mathrm { ft } ^ { 2 }$ 
C)  $1206.4 \mathrm { ft } ^ { 2 }$ 
D)  $25.1 \mathrm { ft } ^ { 2 }$ 
A)  $52.6 \mathrm { ft } ^ { 2 }$ 
B)  $603.2 \mathrm { ft } ^ { 2 }$ 
C)  $1206.4 \mathrm { ft } ^ { 2 }$ 
D)  $25.1 \mathrm { ft } ^ { 2 }$

Question 15

Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
-$- 13 \pi$

Accepted Answer

A)  $- 2520 ^ { \circ }$ 
B)  $- 2340 ^ { \circ }$ 
C)  $- 4680 ^ { \circ }$ 
D)  $- 1170 ^ { \circ }$ 
A)  $- 2520 ^ { \circ }$ 
B)  $- 2340 ^ { \circ }$ 
C)  $- 4680 ^ { \circ }$ 
D)  $- 1170 ^ { \circ }$

Question 16

Solve the problem.
-A rotating beacon is located 3 ft from a wall. The distance from the beacon to the point on the wall where the beacon is aimed is given by
$$a = 3 | \sec 2 \pi t | \text {, }$$
where $t$ is time measured in seconds since the beacon started rotating. Find $a$ for $t = 0.42$ seconds. Round your answer to the nearest hundredth.

Accepted Answer

A)  $- 3.42 \mathrm { ft }$ 
B)  $12.06 \mathrm { ft }$ 
C)  $7.74 \mathrm { ft }$ 
D)  $3.42 \mathrm { ft }$ 
A)  $- 3.42 \mathrm { ft }$ 
B)  $12.06 \mathrm { ft }$ 
C)  $7.74 \mathrm { ft }$ 
D)  $3.42 \mathrm { ft }$

Question 17

Use the formula $s = r \omega t$ to find the value of the missing variable. Give an exact answer.
-$\mathrm { s } = \frac { \pi } { 3 } \mathrm {~m} , \mathrm { r } = 5 \mathrm {~m} , \mathrm { t } = 16 \mathrm { sec }$

Accepted Answer

A)  $240 \pi$ radians per sec 
B)  $\frac { \pi } { 240 }$ radian per sec 
C)  $\frac { 16 \pi } { 15 }$ radian per sec 
D)  $\frac { 15 \pi } { 16 }$ radians per sec 
A)  $240 \pi$ radians per sec 
B)  $\frac { \pi } { 240 }$ radian per sec 
C)  $\frac { 16 \pi } { 15 }$ radian per sec 
D)  $\frac { 15 \pi } { 16 }$ radians per sec

Question 18

Graph the function.
-$y=-\frac{3}{5} \cot \left(\frac{1}{2} x-\frac{\pi}{2}\right)$

Accepted Answer

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

Question 19

Find the specified quantity.
-Find the amplitude of $y = 5 \cos \left( 4 x + \frac { \pi } { 3 } \right)$.

Accepted Answer

A)  4 
B)  5 
C)  $\frac { \pi } { 2 }$ 
D)  20 
A)  4 
B)  5 
C)  $\frac { \pi } { 2 }$ 
D)  20

Question 20

Find the phase shift of the function.
-$$y = 4 \sin \left( 2 x - \frac { \pi } { 2 } \right)$$

Accepted Answer

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

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\csc 0.2756$

Solve the problem. -Find the radius (to the nearest hundredth of a millimeter) of a pulley if rotating the pulley $55.21 ^ { \circ }$ raises the pulley $17.5 \mathrm {~mm}$ .

Graph the function. - $y=\frac{1}{3} \tan \left(\frac{4}{5} x+\frac{\pi}{5}\right)$ $Graph the function. - y=\frac{1}{3} \tan \left(\frac{4}{5} x+\frac{\pi}{5}\right)$

Find the length of an arc intercepted by a central angle θin a circle of radius r. Round your answer to 1 decimal place. - $\mathrm { r } = 10.63 \mathrm {~cm}$ .; $\theta = \frac { 10 } { 9 } \pi$ radians

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

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, $43.15 ^ { \circ } \mathrm { N }$ , are $486 \mathrm {~km}$ apart.

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $43 ^ { \circ }$

Solve the problem. -Find the radius of a circle in which a central angle of $\frac { \pi } { 3 }$ radian determines a sector of area 56 square meters. Round to the nearest hundredth.

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\cot 0.1369$

Graph the function over a one-period interval. - $y=4+2 \sin (x-\pi)$ $Graph the function over a one-period interval. - y=4+2 \sin (x-\pi)$

Find the area of a sector of a circle having radius r and central angle θ. If necessary, express the answer to the nearest tenth. - $\mathrm { r } = 24.0 \mathrm { ft } , \theta = \frac { 2 \pi } { 3 }$ radians

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- 13 \pi$

Use the formula $s = r \omega t$ to find the value of the missing variable. Give an exact answer. - $\mathrm { s } = \frac { \pi } { 3 } \mathrm {~m} , \mathrm { r } = 5 \mathrm {~m} , \mathrm { t } = 16 \mathrm { sec }$

Graph the function. - $y=-\frac{3}{5} \cot \left(\frac{1}{2} x-\frac{\pi}{2}\right)$ $Graph the function. - y=-\frac{3}{5} \cot \left(\frac{1}{2} x-\frac{\pi}{2}\right)$

Find the specified quantity. -Find the amplitude of $y = 5 \cos \left( 4 x + \frac { \pi } { 3 } \right)$ .

Find the phase shift of the function. - $y = 4 \sin \left( 2 x - \frac { \pi } { 2 } \right)$

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

Use a table or a calculator to evaluate the function. Round to four decimal places. - csc⁡0.2756\csc 0.2756csc0.2756

Solve the problem. -Find the radius (to the nearest hundredth of a millimeter) of a pulley if rotating the pulley 55.21∘55.21 ^ { \circ }55.21∘ raises the pulley 17.5 mm17.5 \mathrm {~mm}17.5 mm .

Solve the problem. -Let angle POQ be designated θ\thetaθ . Angles PQR\mathrm { PQR }PQR and VRQ are right angles. If θ=38∘\theta = 38 ^ { \circ }θ=38∘ , find the length of PQ accurate to four decimal places.

Graph the function. - y=13tan⁡(45x+π5)y=\frac{1}{3} \tan \left(\frac{4}{5} x+\frac{\pi}{5}\right)y=31​tan(54​x+5π​)

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=10.63 cm\mathrm { r } = 10.63 \mathrm {~cm}r=10.63 cm .; θ=109π\theta = \frac { 10 } { 9 } \piθ=910​π radians

Find the exact value of s in the given interval that has the given circular function value. - [π2,π];sin⁡s=22\left[ \frac { \pi } { 2 } , \pi \right] ; \sin \mathrm { s } = \frac { \sqrt { 2 } } { 2 }[2π​,π];sins=22​​

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, 43.15∘N43.15 ^ { \circ } \mathrm { N }43.15∘N , are 486 km486 \mathrm {~km}486 km apart.

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 sec⁡θ\sec \thetasecθ .

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - 43∘43 ^ { \circ }43∘

Solve the problem. -Find the radius of a circle in which a central angle of π3\frac { \pi } { 3 }3π​ radian determines a sector of area 56 square meters. Round to the nearest hundredth.

Use a table or a calculator to evaluate the function. Round to four decimal places. - cot⁡0.1369\cot 0.1369cot0.1369

Graph the function over a one-period interval. - y=4+2sin⁡(x−π)y=4+2 \sin (x-\pi)y=4+2sin(x−π)

Find the area of a sector of a circle having radius r and central angle θ. If necessary, express the answer to the nearest tenth. - r=24.0ft,θ=2π3\mathrm { r } = 24.0 \mathrm { ft } , \theta = \frac { 2 \pi } { 3 }r=24.0ft,θ=32π​ radians

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - −13π- 13 \pi−13π

Use the formula s=rωts = r \omega ts=rωt to find the value of the missing variable. Give an exact answer. - s=π3 m,r=5 m,t=16sec\mathrm { s } = \frac { \pi } { 3 } \mathrm {~m} , \mathrm { r } = 5 \mathrm {~m} , \mathrm { t } = 16 \mathrm { sec }s=3π​ m,r=5 m,t=16sec

Graph the function. - y=−35cot⁡(12x−π2)y=-\frac{3}{5} \cot \left(\frac{1}{2} x-\frac{\pi}{2}\right)y=−53​cot(21​x−2π​)

Find the specified quantity. -Find the amplitude of y=5cos⁡(4x+π3)y = 5 \cos \left( 4 x + \frac { \pi } { 3 } \right)y=5cos(4x+3π​) .

Find the phase shift of the function. - y=4sin⁡(2x−π2)y = 4 \sin \left( 2 x - \frac { \pi } { 2 } \right)y=4sin(2x−2π​)

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. - $\csc 0.2756$

Solve the problem. -Find the radius (to the nearest hundredth of a millimeter) of a pulley if rotating the pulley $55.21 ^ { \circ }$ raises the pulley $17.5 \mathrm {~mm}$ .

Graph the function. - $y=\frac{1}{3} \tan \left(\frac{4}{5} x+\frac{\pi}{5}\right)$ $Graph the function. - y=\frac{1}{3} \tan \left(\frac{4}{5} x+\frac{\pi}{5}\right)$

Find the length of an arc intercepted by a central angle θin a circle of radius r. Round your answer to 1 decimal place. - $\mathrm { r } = 10.63 \mathrm {~cm}$ .; $\theta = \frac { 10 } { 9 } \pi$ radians

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

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the latitude of Spokane, WA if Spokane and Jordan Valley, OR, $43.15 ^ { \circ } \mathrm { N }$ , are $486 \mathrm {~km}$ apart.

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $43 ^ { \circ }$

Solve the problem. -Find the radius of a circle in which a central angle of $\frac { \pi } { 3 }$ radian determines a sector of area 56 square meters. Round to the nearest hundredth.

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\cot 0.1369$

Graph the function over a one-period interval. - $y=4+2 \sin (x-\pi)$ $Graph the function over a one-period interval. - y=4+2 \sin (x-\pi)$

Find the area of a sector of a circle having radius r and central angle θ. If necessary, express the answer to the nearest tenth. - $\mathrm { r } = 24.0 \mathrm { ft } , \theta = \frac { 2 \pi } { 3 }$ radians

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- 13 \pi$

Use the formula $s = r \omega t$ to find the value of the missing variable. Give an exact answer. - $\mathrm { s } = \frac { \pi } { 3 } \mathrm {~m} , \mathrm { r } = 5 \mathrm {~m} , \mathrm { t } = 16 \mathrm { sec }$

Graph the function. - $y=-\frac{3}{5} \cot \left(\frac{1}{2} x-\frac{\pi}{2}\right)$ $Graph the function. - y=-\frac{3}{5} \cot \left(\frac{1}{2} x-\frac{\pi}{2}\right)$

Find the specified quantity. -Find the amplitude of $y = 5 \cos \left( 4 x + \frac { \pi } { 3 } \right)$ .

Find the phase shift of the function. - $y = 4 \sin \left( 2 x - \frac { \pi } { 2 } \right)$