Question 1

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
-$48 ^ { \circ }$

Accepted Answer

A)  $0.5378$ 
B)  $0.6378$ 
C)  $0.7378$ 
D)  $0.8378$ 
A)  $0.5378$ 
B)  $0.6378$ 
C)  $0.7378$ 
D)  $0.8378$

Question 2

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

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)  $y = - \cot 2 x$ 
B)  $y = - 2 \tan x$ 
C)  $y = \tan 2 x$ 
D)  $\mathrm { y } = - 2 \cot \mathrm { x }$ 
A)  $y = - \cot 2 x$ 
B)  $y = - 2 \tan x$ 
C)  $y = \tan 2 x$ 
D)  $\mathrm { y } = - 2 \cot \mathrm { x }$

Question 4

Solve the problem.
-A center-pivot irrigation system waters a sector-shaped field. Find the area of the field if the central angle, $\theta = 32 ^ { \circ }$ and the radius, $r = 151$ meters. Round to the nearest whole number.

Accepted Answer

A)  $6367 \mathrm {~m} ^ { 2 }$ 
B)  $84 \mathrm {~m} ^ { 2 }$ 
C)  $42 \mathrm {~m} ^ { 2 }$ 
D)  $12,734 \mathrm {~m} ^ { 2 }$ 
A)  $6367 \mathrm {~m} ^ { 2 }$ 
B)  $84 \mathrm {~m} ^ { 2 }$ 
C)  $42 \mathrm {~m} ^ { 2 }$ 
D)  $12,734 \mathrm {~m} ^ { 2 }$

Question 5

Solve the problem.
-Let angle $P O Q$ be designated $\theta$. Angles $P Q R$ and VRQ are right angles. If $\theta = 11 ^ { \circ }$, find the length of $\mathrm { OV }$ accurate to four decimal places.

Accepted Answer

A)  $0.1908$ 
B)  $0.9816$ 
C)  $1.0187$ 
D)  $5.2408$ 
A)  $0.1908$ 
B)  $0.9816$ 
C)  $1.0187$ 
D)  $5.2408$

Question 6

Solve the problem.
-Let angle $\mathrm { POQ }$ be designated $\theta$. Angles $\mathrm { PQR }$ and VRQ are right angles. If $\theta = 45 ^ { \circ }$, find the exact length of VR.

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $\sqrt { 2 }$ 
C)  0 
D)  1 
A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $\sqrt { 2 }$ 
C)  0 
D)  1

Question 7

Solve the problem.
-Determine the period and frequency of oscillation when a pendulum of length 11 feet is released after being displaced 2 radians. Round constants to 8 decimal places, if necessary.

Accepted Answer

A)  Period $= 11 \pi \mathrm { sec }$, frequency $= \frac { 1 } { 11 \pi }$ cycles per sec 
B)  Period $= 2 \pi \sqrt { 2.90909091 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 0.34375 }$ cycles per sec 
C)  Period $= 2 \pi \sqrt { 0.34375 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 2.90909091 }$ cycles per sec 
D)  Period $= \frac { \pi } { 11 }$ sec, frequency $= \frac { 11 } { \pi }$ cycles per sec 
A)  Period $= 11 \pi \mathrm { sec }$, frequency $= \frac { 1 } { 11 \pi }$ cycles per sec 
B)  Period $= 2 \pi \sqrt { 2.90909091 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 0.34375 }$ cycles per sec 
C)  Period $= 2 \pi \sqrt { 0.34375 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 2.90909091 }$ cycles per sec 
D)  Period $= \frac { \pi } { 11 }$ sec, frequency $= \frac { 11 } { \pi }$ cycles per sec

Question 8

Match the function with its graph.
-1) $y = - \tan \left( x - \frac { \pi } { 2 } \right)$ 2) $y = \tan \left( x + \frac { \pi } { 2 } \right\}$
3) $y = - \cot \left( x - \frac { \pi } { 2 } \right\}$ 4) $y = \cot \left( x + \frac { \pi } { 2 } \right\}$
A.
 
B.
 
C.
 
D.

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Solve the problem.
-A pendulum of length $14.6$ inches swings $5 ^ { \circ } 27 ^ { \prime }$ to each side of its vertical position. What is the length (to the nearest hundredth of an inch) of the arc through which the end of the pendulum swings?

Accepted Answer

A)  $2.58 \mathrm { in }$. 
B)  $2.78 \mathrm { in }$. 
C)  $2.68 \mathrm { in } .$ 
D)  $2.48 \mathrm { in }$. 
A)  $2.58 \mathrm { in }$. 
B)  $2.78 \mathrm { in }$. 
C)  $2.68 \mathrm { in } .$ 
D)  $2.48 \mathrm { in }$.

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Find the exact circular function value.
-$$\sin \frac { 4 \pi } { 3 }$$

Accepted Answer

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

Question 14

Solve the problem.
-Suppose the tip of the minute hand of a clock is 4 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact answer.

Accepted Answer

A)  $4 \pi \mathrm { in }$. 
B)  $2 \pi \mathrm { in }$. 
C)  $8 \pi \mathrm { in }$. 
D)  $16 \pi$ in. 
A)  $4 \pi \mathrm { in }$. 
B)  $2 \pi \mathrm { in }$. 
C)  $8 \pi \mathrm { in }$. 
D)  $16 \pi$ in.

Question 15

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated.
-$\mathrm { v } = 16 \mathrm { ft }$ per sec, $\mathrm { r } = 9.3 \mathrm { ft }$ (Round to four decimal places when necessary.)

Accepted Answer

A)  $0.5813$ radian per sec 
B)  $5.0929$ radians per sec 
C)  $1.7204$ radians per sec 
D)  $0.3378$ radian per sec 
A)  $0.5813$ radian per sec 
B)  $5.0929$ radians per sec 
C)  $1.7204$ radians per sec 
D)  $0.3378$ radian per sec

Question 16

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
-$32.2094 ^ { \circ }$

Accepted Answer

A)  $0.7622$ 
B)  $0.4622$ 
C)  $0.6622$ 
D)  $0.5622$ 
A)  $0.7622$ 
B)  $0.4622$ 
C)  $0.6622$ 
D)  $0.5622$

Question 17

Use a table or a calculator to evaluate the function. Round to four decimal places.
-$\cos 0.2921$

Accepted Answer

A)  $1.0442$ 
B)  $0.9576$ 
C)  $0.2880$ 
D)  $0.3007$ 
A)  $1.0442$ 
B)  $0.9576$ 
C)  $0.2880$ 
D)  $0.3007$

Question 18

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places.
-$\csc \mathrm { s } = 1.7345$

Accepted Answer

A)  $0.7145$ 
B)  $0.5145$ 
C)  $0.6145$ 
D)  $0.4145$ 
A)  $0.7145$ 
B)  $0.5145$ 
C)  $0.6145$ 
D)  $0.4145$

Question 19

Find the corresponding angle measure in radians.
-$$- 240 ^ { \circ }$$

Accepted Answer

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

Question 20

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

Accepted Answer

A)  $1.57 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $\frac { \pi } { 2 } \circ$ 
D)  $90 \pi ^ { \circ }$ 
A)  $1.57 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $\frac { \pi } { 2 } \circ$ 
D)  $90 \pi ^ { \circ }$

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $48 ^ { \circ }$

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 center-pivot irrigation system waters a sector-shaped field. Find the area of the field if the central angle, $\theta = 32 ^ { \circ }$ and the radius, $r = 151$ meters. Round to the nearest whole number.

Solve the problem. -Determine the period and frequency of oscillation when a pendulum of length 11 feet is released after being displaced 2 radians. Round constants to 8 decimal places, if necessary.

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

Solve the problem. -A pendulum of length $14.6$ inches swings $5 ^ { \circ } 27 ^ { \prime }$ to each side of its vertical position. What is the length (to the nearest hundredth of an inch) of the arc through which the end of the pendulum swings?

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

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

Find the exact circular function value. - $\sin \frac { 4 \pi } { 3 }$

Solve the problem. -Suppose the tip of the minute hand of a clock is 4 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact answer.

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\mathrm { v } = 16 \mathrm { ft }$ per sec, $\mathrm { r } = 9.3 \mathrm { ft }$ (Round to four decimal places when necessary.)

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $32.2094 ^ { \circ }$

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\cos 0.2921$

Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places. - $\csc \mathrm { s } = 1.7345$

Find the corresponding angle measure in radians. - $- 240 ^ { \circ }$ $Find the corresponding angle measure in radians. - - 240 ^ { \circ }$

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

Equations and Inequalities

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Exam 6: The Circular Functions and Their Graphs

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - 48∘48 ^ { \circ }48∘

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 .

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 center-pivot irrigation system waters a sector-shaped field. Find the area of the field if the central angle, θ=32∘\theta = 32 ^ { \circ }θ=32∘ and the radius, r=151r = 151r=151 meters. Round to the nearest whole number.

Solve the problem. -Let angle POQP O QPOQ be designated θ\thetaθ . Angles PQRP Q RPQR and VRQ are right angles. If θ=11∘\theta = 11 ^ { \circ }θ=11∘ , find the length of OV\mathrm { OV }OV accurate to four decimal places.

Solve the problem. -Let angle POQ\mathrm { POQ }POQ be designated θ\thetaθ . Angles PQR\mathrm { PQR }PQR and VRQ are right angles. If θ=45∘\theta = 45 ^ { \circ }θ=45∘ , find the exact length of VR.