Question 1

Find the value of the arc length when $\theta$ (the central Angle) is given in degrees instead of 
radians.

Accepted Answer

The answer of Find the value of the arc length...

Question 2

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

Accepted Answer

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

Question 3

Graph the function over a one-period interval.
-A pendulum of length L, when displaced horizontally and released, oscillates with harmonic motion according to the equation $y = A \sin ( ( \sqrt { g / L } ) t + \pi / 2 )$, where $y$ is the distance in meters from the rest position $t$ seconds after release, and $g = 9.8 \mathrm {~m} / \mathrm { sec } ^ { 2 }$. Identify the period, amplitude, and phase shift when $\mathrm { A } = 0.32 \mathrm {~m}$ and $\mathrm { L } = 0.39 \mathrm {~m}$. Round all answers to the nearest hundredth.

Accepted Answer

A)  $1.26 \mathrm { sec } , 0.32 \mathrm {~m} , 0.31$ units to the right 
B)  $0.63 \mathrm { sec } , 0.32 \mathrm {~m} , - 0.63$ units to the left 
C)  $0.25 \mathrm { sec } , 0.32 \mathrm {~m} , - 0.063$ units to the left 
D)  $1.26 \mathrm { sec } , 0.32 \mathrm {~m} , - 0.31$ units to the left 
A)  $1.26 \mathrm { sec } , 0.32 \mathrm {~m} , 0.31$ units to the right 
B)  $0.63 \mathrm { sec } , 0.32 \mathrm {~m} , - 0.63$ units to the left 
C)  $0.25 \mathrm { sec } , 0.32 \mathrm {~m} , - 0.063$ units to the left 
D)  $1.26 \mathrm { sec } , 0.32 \mathrm {~m} , - 0.31$ units to the left

Question 4

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)  $- \frac { 24 } { 7 }$ 
B)  $\frac { 7 } { 24 }$ 
C)  $\frac { 24 } { 7 }$ 
D)  $- \frac { 7 } { 24 }$ 
A)  $- \frac { 24 } { 7 }$ 
B)  $\frac { 7 } { 24 }$ 
C)  $\frac { 24 } { 7 }$ 
D)  $- \frac { 7 } { 24 }$

Question 5

Approximate the length using the formula for arc length. Round to the nearest meter.
-A television tower $420 \mathrm {~m}$ high subtends an angle of $4 ^ { \circ } 40 ^ { \prime }$. How far away is the tower?

Accepted Answer

A)  $6720 \mathrm {~m}$ 
B)  $5157 \mathrm {~m}$ 
C)  $6760 \mathrm {~m}$ 
D)  $5197 \mathrm {~m}$ 
A)  $6720 \mathrm {~m}$ 
B)  $5157 \mathrm {~m}$ 
C)  $6760 \mathrm {~m}$ 
D)  $5197 \mathrm {~m}$

Question 6

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$
-$390 ^ { \circ }$

Accepted Answer

A)  $\frac { 13 \pi } { 3 }$ 
B)  $\frac { 13 \pi } { 5 }$ 
C)  $\frac { 13 \pi } { 12 }$ 
D)  $\frac { 13 \pi } { 6 }$ 
A)  $\frac { 13 \pi } { 3 }$ 
B)  $\frac { 13 \pi } { 5 }$ 
C)  $\frac { 13 \pi } { 12 }$ 
D)  $\frac { 13 \pi } { 6 }$

Question 7

Solve the problem
-Let angle $\mathrm { POQ }$ be designated $\theta$. Angles $\mathrm { PQR }$ and VRQ are right angles. If $\theta = 70 ^ { \circ }$, find the length of $\mathrm { OQ }$ accurate to four decimal places.

Accepted Answer

A)  $0.9397$ 
B)  $0.3420$ 
C)  $2.7475$ 
D)  $2.9238$ 
A)  $0.9397$ 
B)  $0.3420$ 
C)  $2.7475$ 
D)  $2.9238$

Question 8

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

Accepted Answer

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

Question 9

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$
-$288 ^ { \circ }$

Accepted Answer

A)  $\frac { 4 \pi } { 5 }$ 
B)  $\frac { 8 \pi } { 5 }$ 
C)  $\frac { 9 \pi } { 5 }$ 
D)  $\frac { 16 \pi } { 5 }$ 
A)  $\frac { 4 \pi } { 5 }$ 
B)  $\frac { 8 \pi } { 5 }$ 
C)  $\frac { 9 \pi } { 5 }$ 
D)  $\frac { 16 \pi } { 5 }$

Question 10

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)  $y = 4 \cos \left( \frac { 1 } { 3 } x \right)$ 
B)  $y = 4 \sin \left( \frac { 1 } { 3 } x \right)$ 
C)  $y = - 4 \cos ( 3 x )$ 
D)  $y = 4 \cos ( 3 x )$ 
A)  $y = 4 \cos \left( \frac { 1 } { 3 } x \right)$ 
B)  $y = 4 \sin \left( \frac { 1 } { 3 } x \right)$ 
C)  $y = - 4 \cos ( 3 x )$ 
D)  $y = 4 \cos ( 3 x )$

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Solve the problem
-$\mathrm { r } = 2 \mathrm {~cm} , \omega = \frac { \pi } { 11 }$ radian per sec, $\mathrm { t } = 2 \mathrm { sec }$

Accepted Answer

A)  $\frac { 11 \pi } { 4 } \mathrm {~cm}$ 
B)  $\frac { 4 } { 11 \pi } \mathrm { cm }$ 
C)  $\frac { 11 } { 4 \pi } \mathrm { cm }$ 
D)  $\frac { 4 \pi } { 11 } \mathrm {~cm}$ 
A)  $\frac { 11 \pi } { 4 } \mathrm {~cm}$ 
B)  $\frac { 4 } { 11 \pi } \mathrm { cm }$ 
C)  $\frac { 11 } { 4 \pi } \mathrm { cm }$ 
D)  $\frac { 4 \pi } { 11 } \mathrm {~cm}$

Question 14

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$
-$36 ^ { \circ }$

Accepted Answer

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

Question 15

Determine the equation of the graph.
-

Accepted Answer

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

Question 16

Determine the equation of the graph.
-Determine the period and frequency of oscillation when a pendulum of length 7 feet is released after being displaced 2 radians. Round constants to 8 decimal places, if necessary.

Accepted Answer

A)  Period $= 2 \pi \sqrt { 0.21875 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 4.57142857 }$ cycles per sec 
B)  Period $= 2 \pi \sqrt { 4.57142857 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 0.21875 }$ cycles per sec 
C)  Period $= 7 \pi \mathrm { sec }$, frequency $= \frac { 1 } { 7 \pi }$ cycles per sec 
D)  Period $= \frac { \pi } { 7 }$ sec, frequency $= \frac { 7 } { \pi }$ cycles per sec 
A)  Period $= 2 \pi \sqrt { 0.21875 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 4.57142857 }$ cycles per sec 
B)  Period $= 2 \pi \sqrt { 4.57142857 }$ sec, frequency $= \frac { 1 } { 2 \pi } \sqrt { 0.21875 }$ cycles per sec 
C)  Period $= 7 \pi \mathrm { sec }$, frequency $= \frac { 1 } { 7 \pi }$ cycles per sec 
D)  Period $= \frac { \pi } { 7 }$ sec, frequency $= \frac { 7 } { \pi }$ cycles per sec

Question 17

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
-A bicycle with a 26-inch wheel (diameter) travels a distance of 300 feet. How many revolutions does the wheel make (to the nearest revolution)?

Accepted Answer

A)  88 revolutions 
B)  44 revolutions 
C)  82 revolutions 
D)  38 revolutions 
A)  88 revolutions 
B)  44 revolutions 
C)  82 revolutions 
D)  38 revolutions

Question 18

Determine the equation of the graph.
-Suppose that a weight on a spring has an initial position of $s ( 0 ) = 6$ inches and a period of $\mathrm { P } = 2.5$ seconds. Find a function $\mathrm { s } ( \mathrm { t } ) = \mathrm { a } \cos ( 2 \pi \mathrm { Ft } )$ that models the displacement of the weight.

Accepted Answer

A)  $s ( t ) = 12 \cos ( 2 \pi ( 2.5 ) t )$ 
B)  $\mathrm { s } ( \mathrm { t } ) = 12 \cos ( 2 \pi ( 0.4 ) \mathrm { t } )$ 
C)  $s ( t ) = 6 \cos ( 2 \pi ( 2.5 ) t )$ 
D)  $s ( t ) = 6 \cos ( 2 \pi ( 0.4 ) t )$ 
A)  $s ( t ) = 12 \cos ( 2 \pi ( 2.5 ) t )$ 
B)  $\mathrm { s } ( \mathrm { t } ) = 12 \cos ( 2 \pi ( 0.4 ) \mathrm { t } )$ 
C)  $s ( t ) = 6 \cos ( 2 \pi ( 2.5 ) t )$ 
D)  $s ( t ) = 6 \cos ( 2 \pi ( 0.4 ) t )$

Question 19

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

Accepted Answer

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

Question 20

Convert the degree measure to radians, correct to four decimal places. $$3.1416 \text { for } \pi \text {. }$$
-$50.97 ^ { \circ }$

Accepted Answer

A)  $0.9896$ 
B)  $0.7896$ 
C)  $0.6896$ 
D)  $0.8896$ 
A)  $0.9896$ 
B)  $0.7896$ 
C)  $0.6896$ 
D)  $0.8896$

Find the value of the arc length when $\theta$ (the central Angle) is given in degrees instead of radians.

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

Approximate the length using the formula for arc length. Round to the nearest meter. -A television tower $420 \mathrm {~m}$ high subtends an angle of $4 ^ { \circ } 40 ^ { \prime }$ . How far away is the tower?

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $390 ^ { \circ }$

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

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $288 ^ { \circ }$

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

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

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

Solve the problem - $\mathrm { r } = 2 \mathrm {~cm} , \omega = \frac { \pi } { 11 }$ radian per sec, $\mathrm { t } = 2 \mathrm { sec }$

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $36 ^ { \circ }$

Determine the equation of the graph. -

Determine the equation of the graph. -Determine the period and frequency of oscillation when a pendulum of length 7 feet is released after being displaced 2 radians. Round constants to 8 decimal places, if necessary.

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -A bicycle with a 26-inch wheel (diameter) travels a distance of 300 feet. How many revolutions does the wheel make (to the nearest revolution)?

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

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $50.97 ^ { \circ }$

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

Find the value of the arc length when θ\thetaθ (the central Angle) is given in degrees instead of radians.

Graph the function. - y=23tan⁡xy = \frac { 2 } { 3 } \tan xy=32​tanx

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

Approximate the length using the formula for arc length. Round to the nearest meter. -A television tower 420 m420 \mathrm {~m}420 m high subtends an angle of 4∘40′4 ^ { \circ } 40 ^ { \prime }4∘40′ . How far away is the tower?

Convert the degree measure to radians. Leave answer as a multiple of π.\pi .π. - 390∘390 ^ { \circ }390∘

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=70∘\theta = 70 ^ { \circ }θ=70∘ , find the length of OQ\mathrm { OQ }OQ accurate to four decimal places.

Graph the function. - y=3cos⁡(x+π4)y = 3 \cos \left( x + \frac { \pi } { 4 } \right)y=3cos(x+4π​)

Convert the degree measure to radians. Leave answer as a multiple of π.\pi .π. - 288∘288 ^ { \circ }288∘

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. -

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

Graph the function. - y=2sin⁡14xy=2 \sin \frac{1}{4} xy=2sin41​x

Solve the problem - r=2 cm,ω=π11\mathrm { r } = 2 \mathrm {~cm} , \omega = \frac { \pi } { 11 }r=2 cm,ω=11π​ radian per sec, t=2sec\mathrm { t } = 2 \mathrm { sec }t=2sec

Convert the degree measure to radians. Leave answer as a multiple of π.\pi .π. - 36∘36 ^ { \circ }36∘

Determine the equation of the graph. -

Determine the equation of the graph. -Determine the period and frequency of oscillation when a pendulum of length 7 feet is released after being displaced 2 radians. Round constants to 8 decimal places, if necessary.

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -A bicycle with a 26-inch wheel (diameter) travels a distance of 300 feet. How many revolutions does the wheel make (to the nearest revolution)?

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

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. - 50.97∘50.97 ^ { \circ }50.97∘

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

Find the value of the arc length when $\theta$ (the central Angle) is given in degrees instead of radians.

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

Approximate the length using the formula for arc length. Round to the nearest meter. -A television tower $420 \mathrm {~m}$ high subtends an angle of $4 ^ { \circ } 40 ^ { \prime }$ . How far away is the tower?

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $390 ^ { \circ }$

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

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $288 ^ { \circ }$

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

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

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

Solve the problem - $\mathrm { r } = 2 \mathrm {~cm} , \omega = \frac { \pi } { 11 }$ radian per sec, $\mathrm { t } = 2 \mathrm { sec }$

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $36 ^ { \circ }$

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

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $50.97 ^ { \circ }$