Question 1

Use a calculator to solve for x in the given interval
-$\sec \theta = 1.77,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Accepted Answer

A)  $55.60 ^ { \circ }$ 
B)  $- 29.47 ^ { \circ }$ 
C)  $34.40 ^ { \circ }$ 
D)  $29.47 ^ { \circ }$ 
A)  $55.60 ^ { \circ }$ 
B)  $- 29.47 ^ { \circ }$ 
C)  $34.40 ^ { \circ }$ 
D)  $29.47 ^ { \circ }$

Question 2

Solve the problem.
-The position of a weight attached to a spring is $s ( t ) = - 8 \cos 24 \pi t$ inches after $t$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?

Accepted Answer

A)  The maximum height of 16 inches is first reached after 12 seconds. 
B)  The maximum height of 8 inches is first reached after $0.04$ seconds. 
C)  The maximum height of 8 inches is first reached after 12 seconds. 
D)  The maximum height of 16 inches is first reached after 6 seconds. 
A)  The maximum height of 16 inches is first reached after 12 seconds. 
B)  The maximum height of 8 inches is first reached after $0.04$ seconds. 
C)  The maximum height of 8 inches is first reached after 12 seconds. 
D)  The maximum height of 16 inches is first reached after 6 seconds.

Question 3

Determine whether the given function is positive or negative for values of t in the specified quadrant.
-Quadrant III, sec t

Accepted Answer

A)  Positive 
B)  Negative 
A)  Positive 
B)  Negative

Question 4

Solve the problem.
-The air speed of an airplane is $640 \mathrm {~km} / \mathrm { hr }$ and its angle of climb is $9.13 ^ { \circ }$. What is its ground speed (to the nearest $\mathrm { km } / \mathrm { hr } )$ ?

Accepted Answer

A)  $632 \mathrm {~km} / \mathrm { hr }$ 
B)  $617 \mathrm {~km} / \mathrm { hr }$ 
C)  $622 \mathrm {~km} / \mathrm { hr }$ 
D)  $627 \mathrm {~km} / \mathrm { hr }$ 
A)  $632 \mathrm {~km} / \mathrm { hr }$ 
B)  $617 \mathrm {~km} / \mathrm { hr }$ 
C)  $622 \mathrm {~km} / \mathrm { hr }$ 
D)  $627 \mathrm {~km} / \mathrm { hr }$

Question 5

Choose the point on the terminal side of .
-$$\theta = 240 ^ { \circ }$$

Accepted Answer

A)  $( - \sqrt { 3 } , 1 )$ 
B)  $( - 1 , \sqrt { 3 } )$ 
C)  $( - 1 , - \sqrt { 3 } )$ 
D)  $( - \sqrt { 3 } , - 1 )$ 
A)  $( - \sqrt { 3 } , 1 )$ 
B)  $( - 1 , \sqrt { 3 } )$ 
C)  $( - 1 , - \sqrt { 3 } )$ 
D)  $( - \sqrt { 3 } , - 1 )$

Question 6

Determine the sign (positive or negative) of the given value without use of a calculator.
-$$\sin \left( - \frac { \pi } { 9 } \right)$$

Accepted Answer

A)  Positive 
B)  Negative 
A)  Positive 
B)  Negative

Question 7

Determine the sign (positive or negative) of the given value without use of a calculator.
-$\tan \frac { \pi } { 9 }$

Accepted Answer

A)  Positive 
B)  Negative 
A)  Positive 
B)  Negative

Question 8

Solve the problem.
-A racetracks curve is banked so that the outside of the curve is slightly elevated or inclined above the inside of the curve. This inclination is called the elevation of the track. The maximum speed on the track in miles per hour is given by
$$\sqrt { r ( 29000 + 41000 \tan \theta ) }$$
where $r$ is the radius of the track in miles and $\theta$ is the elevation in degrees. Find the maximum speed for a racetracks with an elevation of $27 ^ { \circ }$ and a radius of $0.5$ miles. Round to the nearest mile per hour.

Accepted Answer

A)  35,278 miles per hour 
B)  $- 74,403$ miles per hour 
C)  158 miles per hour 
D)  188 miles per hour 
A)  35,278 miles per hour 
B)  $- 74,403$ miles per hour 
C)  158 miles per hour 
D)  188 miles per hour

Question 9

Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$\cos \theta = \frac { 10 } { 11 } ; \tan \theta$

Accepted Answer

A)  $\frac { \sqrt { 21 } } { 11 }$ 
B)  $\frac { 11 } { 10 }$ 
C)  $\frac { 10 } { \sqrt { 21 } }$ 
D)  $\frac { \sqrt { 21 } } { 10 }$ 
A)  $\frac { \sqrt { 21 } } { 11 }$ 
B)  $\frac { 11 } { 10 }$ 
C)  $\frac { 10 } { \sqrt { 21 } }$ 
D)  $\frac { \sqrt { 21 } } { 10 }$

Question 10

Find the trigonometric function value for the angle shown.
-$\tan \theta$

Accepted Answer

A)  $\tan \theta = \frac { - \sqrt { 33 } } { 4 }$ 
B)  $\tan \theta = \frac { - 4 } { 7 }$ 
C)  $\tan \theta = \frac { - \sqrt { 33 } } { 7 }$ 
D)  $\tan \theta = \frac { - 4 \sqrt { 33 } } { 33 }$ 
A)  $\tan \theta = \frac { - \sqrt { 33 } } { 4 }$ 
B)  $\tan \theta = \frac { - 4 } { 7 }$ 
C)  $\tan \theta = \frac { - \sqrt { 33 } } { 7 }$ 
D)  $\tan \theta = \frac { - 4 \sqrt { 33 } } { 33 }$

Question 11

Choose the graph which matches the function.
-$$y = 2 \cos 2 x - 5 \cos 3 x$$

Accepted Answer

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

Question 12

Solve the problem.
-From a boat on the lake, the angle of elevation to the top of a cliff is $24 ^ { \circ } 11 ^ { \prime }$. If the base of the cliff is 2696 feet from the boat, how high is the cliff (to the nearest foot)?

Accepted Answer

A)  $1214 \mathrm { ft }$ 
B)  $1211 \mathrm { ft }$ 
C)  $1224 \mathrm { ft }$ 
D)  $1221 \mathrm { ft }$ 
A)  $1214 \mathrm { ft }$ 
B)  $1211 \mathrm { ft }$ 
C)  $1224 \mathrm { ft }$ 
D)  $1221 \mathrm { ft }$

Question 13

Find the value of the unique real number between 0 and 2 that satisfies the given conditions.
-$\cos \theta = - \frac { \sqrt { 2 } } { 2 }$ and $\tan \theta < 0$

Accepted Answer

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

Question 14

Determine the sign (positive or negative) of the given value without use of a calculator.
-$\sin 120 ^ { \circ }$

Accepted Answer

A)  Negative 
B)  Positive 
A)  Negative 
B)  Positive

Question 15

Write the word or phrase that best completes each statement or answers the question.
Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, asymptotes, and end behavior.
-f(x) = 2 csc (x/2)

Accepted Answer

Domain: All reals except even multiples

Question 16

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
-$\frac { 8 \pi } { 5 }$

Accepted Answer

A)  $\frac { 18 \pi } { 5 } ; - \frac { 2 \pi } { 5 }$ 
B)  $\frac { 13 \pi } { 5 } ; - \frac { 13 \pi } { 5 }$ 
C)  $\frac { 13 \pi } { 5 } ; - \frac { 2 \pi } { 5 }$ 
D)  $\frac { 2 \pi } { 5 } ; - \frac { 18 \pi } { 5 }$ 
A)  $\frac { 18 \pi } { 5 } ; - \frac { 2 \pi } { 5 }$ 
B)  $\frac { 13 \pi } { 5 } ; - \frac { 13 \pi } { 5 }$ 
C)  $\frac { 13 \pi } { 5 } ; - \frac { 2 \pi } { 5 }$ 
D)  $\frac { 2 \pi } { 5 } ; - \frac { 18 \pi } { 5 }$

Question 17

Describe the end behavior of the function.
-$$f ( x ) = 2 ^ { - x } \sin 5 x$$

Accepted Answer

A)  $\lim _ { x \rightarrow\infty } f ( x ) = \infty$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = 0$ 
C)  $\lim _ { x \rightarrow \infty } f ( x ) = \infty$ 
D)  $\lim _ { x \rightarrow\infty } f ( x ) = 0$ 
A)  $\lim _ { x \rightarrow\infty } f ( x ) = \infty$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = 0$ 
C)  $\lim _ { x \rightarrow \infty } f ( x ) = \infty$ 
D)  $\lim _ { x \rightarrow\infty } f ( x ) = 0$

Question 18

Solve for x in the given interval.
-$\cot x = \sqrt { 3 } , \pi \leq x \leq \frac { 3 \pi } { 2 }$

Accepted Answer

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

Question 19

Solve the problem.
-Use a tangent function to estimate the grade resistance of a 2400 -lb car travelling on a $1.1 ^ { \circ }$ grade. Round your answer to the nearest pound.

Accepted Answer

A)  2358 pounds 
B)  92 pounds 
C)  4715 pounds 
D)  46 pounds 
A)  2358 pounds 
B)  92 pounds 
C)  4715 pounds 
D)  46 pounds

Question 20

Determine the sign (positive or negative) of the given value without use of a calculator.
-$\cos 128 ^ { \circ }$

Accepted Answer

A)  Negative 
B)  Positive 
A)  Negative 
B)  Positive

Use a calculator to solve for x in the given interval - $\sec \theta = 1.77,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Solve the problem. -The position of a weight attached to a spring is $s ( t ) = - 8 \cos 24 \pi t$ inches after $t$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant III, sec t

Solve the problem. -The air speed of an airplane is $640 \mathrm {~km} / \mathrm { hr }$ and its angle of climb is $9.13 ^ { \circ }$ . What is its ground speed (to the nearest $\mathrm { km } / \mathrm { hr } )$ ?

Choose the point on the terminal side of . - $\theta = 240 ^ { \circ }$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\sin \left( - \frac { \pi } { 9 } \right)$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\tan \frac { \pi } { 9 }$

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\cos \theta = \frac { 10 } { 11 } ; \tan \theta$

Find the trigonometric function value for the angle shown. - $\tan \theta$ $Find the trigonometric function value for the angle shown. - \tan \theta$

Choose the graph which matches the function. - $y = 2 \cos 2 x - 5 \cos 3 x$

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is $24 ^ { \circ } 11 ^ { \prime }$ . If the base of the cliff is 2696 feet from the boat, how high is the cliff (to the nearest foot)?

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - $\cos \theta = - \frac { \sqrt { 2 } } { 2 }$ and $\tan \theta < 0$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\sin 120 ^ { \circ }$

Write the word or phrase that best completes each statement or answers the question. Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, asymptotes, and end behavior. -f(x) = 2 csc (x/2)

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $\frac { 8 \pi } { 5 }$

Describe the end behavior of the function. - $f ( x ) = 2 ^ { - x } \sin 5 x$

Solve for x in the given interval. - $\cot x = \sqrt { 3 } , \pi \leq x \leq \frac { 3 \pi } { 2 }$

Solve the problem. -Use a tangent function to estimate the grade resistance of a 2400 -lb car travelling on a $1.1 ^ { \circ }$ grade. Round your answer to the nearest pound.

Determine the sign (positive or negative) of the given value without use of a calculator. - $\cos 128 ^ { \circ }$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 4: Trigonometric Functions

Use a calculator to solve for x in the given interval - sec⁡θ=1.77,0∘≤θ≤90∘\sec \theta = 1.77,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }secθ=1.77,0∘≤θ≤90∘

Solve the problem. -The position of a weight attached to a spring is s(t)=−8cos⁡24πts ( t ) = - 8 \cos 24 \pi ts(t)=−8cos24πt inches after ttt seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant III, sec t

Solve the problem. -The air speed of an airplane is 640 km/hr640 \mathrm {~km} / \mathrm { hr }640 km/hr and its angle of climb is 9.13∘9.13 ^ { \circ }9.13∘ . What is its ground speed (to the nearest km/hr)\mathrm { km } / \mathrm { hr } )km/hr) ?

Choose the point on the terminal side of . - θ=240∘\theta = 240 ^ { \circ }θ=240∘

Determine the sign (positive or negative) of the given value without use of a calculator. - sin⁡(−π9)\sin \left( - \frac { \pi } { 9 } \right)sin(−9π​)

Determine the sign (positive or negative) of the given value without use of a calculator. - tan⁡π9\tan \frac { \pi } { 9 }tan9π​

Assume that θ \theta θ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - cos⁡θ=1011;tan⁡θ\cos \theta = \frac { 10 } { 11 } ; \tan \thetacosθ=1110​;tanθ

Find the trigonometric function value for the angle shown. - tan⁡θ\tan \thetatanθ

Choose the graph which matches the function. - y=2cos⁡2x−5cos⁡3xy = 2 \cos 2 x - 5 \cos 3 xy=2cos2x−5cos3x

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is 24∘11′24 ^ { \circ } 11 ^ { \prime }24∘11′ . If the base of the cliff is 2696 feet from the boat, how high is the cliff (to the nearest foot)?

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - cos⁡θ=−22\cos \theta = - \frac { \sqrt { 2 } } { 2 }cosθ=−22​​ and tan⁡θ<0\tan \theta < 0tanθ<0

Determine the sign (positive or negative) of the given value without use of a calculator. - sin⁡120∘\sin 120 ^ { \circ }sin120∘

Write the word or phrase that best completes each statement or answers the question. Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, asymptotes, and end behavior. -f(x) = 2 csc (x/2)

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - 8π5\frac { 8 \pi } { 5 }58π​

Describe the end behavior of the function. - f(x)=2−xsin⁡5xf ( x ) = 2 ^ { - x } \sin 5 xf(x)=2−xsin5x

Solve for x in the given interval. - cot⁡x=3,π≤x≤3π2\cot x = \sqrt { 3 } , \pi \leq x \leq \frac { 3 \pi } { 2 }cotx=3​,π≤x≤23π​

Solve the problem. -Use a tangent function to estimate the grade resistance of a 2400 -lb car travelling on a 1.1∘1.1 ^ { \circ }1.1∘ grade. Round your answer to the nearest pound.

Determine the sign (positive or negative) of the given value without use of a calculator. - cos⁡128∘\cos 128 ^ { \circ }cos128∘

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Use a calculator to solve for x in the given interval - $\sec \theta = 1.77,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Solve the problem. -The position of a weight attached to a spring is $s ( t ) = - 8 \cos 24 \pi t$ inches after $t$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?

Solve the problem. -The air speed of an airplane is $640 \mathrm {~km} / \mathrm { hr }$ and its angle of climb is $9.13 ^ { \circ }$ . What is its ground speed (to the nearest $\mathrm { km } / \mathrm { hr } )$ ?

Choose the point on the terminal side of . - $\theta = 240 ^ { \circ }$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\sin \left( - \frac { \pi } { 9 } \right)$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\tan \frac { \pi } { 9 }$

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\cos \theta = \frac { 10 } { 11 } ; \tan \theta$

Find the trigonometric function value for the angle shown. - $\tan \theta$ $Find the trigonometric function value for the angle shown. - \tan \theta$

Choose the graph which matches the function. - $y = 2 \cos 2 x - 5 \cos 3 x$

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is $24 ^ { \circ } 11 ^ { \prime }$ . If the base of the cliff is 2696 feet from the boat, how high is the cliff (to the nearest foot)?

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - $\cos \theta = - \frac { \sqrt { 2 } } { 2 }$ and $\tan \theta < 0$

Determine the sign (positive or negative) of the given value without use of a calculator. - $\sin 120 ^ { \circ }$

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $\frac { 8 \pi } { 5 }$

Describe the end behavior of the function. - $f ( x ) = 2 ^ { - x } \sin 5 x$

Solve for x in the given interval. - $\cot x = \sqrt { 3 } , \pi \leq x \leq \frac { 3 \pi } { 2 }$

Solve the problem. -Use a tangent function to estimate the grade resistance of a 2400 -lb car travelling on a $1.1 ^ { \circ }$ grade. Round your answer to the nearest pound.

Determine the sign (positive or negative) of the given value without use of a calculator. - $\cos 128 ^ { \circ }$