Question 1

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined."
-$\sin 1170 ^ { \circ }$

Accepted Answer

A)  1 
B)  0 
C)  undefined 
D)  $- 1$ 
A)  1 
B)  0 
C)  undefined 
D)  $- 1$

Question 2

Evaluate without using a calculator.
-$\cos \omega$, if $\tan \omega = - \frac { 8 } { 5 }$ and $\sin \omega > 0$

Accepted Answer

A)  $ -\frac{\sqrt{89}}{5} $ 
B)  $ \frac{\sqrt{89}}{8} $ 
C)  $ -\frac{5 \sqrt{89}}{89} $ 
D)  $ \frac{5 \sqrt{89}}{89} $ 
A)  $ -\frac{\sqrt{89}}{5} $ 
B)  $ \frac{\sqrt{89}}{8} $ 
C)  $ -\frac{5 \sqrt{89}}{89} $ 
D)  $ \frac{5 \sqrt{89}}{89} $

Question 3

Graph the expression $\sec ^ { 2 } x - \sec ^ { 2 } x \sin ^ { 2 } x$ on your calculator. Determine what constant or single circular function is equivalent to the given expression.

Accepted Answer

The answer of Graph the expression \(\sec ^ { 2...

Question 4

Evaluate without using a calculator by using ratios in a reference triangle.
-$\sec 150 ^ { \circ }$

Accepted Answer

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

Question 5

Solve.
-A rotating beacon is located a distance $\mathrm { d }$ from a long wall. The distance $\mathrm { d }$ is given by $\mathrm { d } = 8$ tan $2 \pi \mathrm { t }$, where $t$ is the time measured in seconds since the beacon started rotating. Solve the equation for $t$.

Accepted Answer

A)  $t = \frac { 1 } { 2 \pi } \tan \frac { d } { 8 }$ 
B)  $t = \frac { 1 } { 2 \pi } \arctan \frac { d } { 8 }$ 
C)  $t = 2 \pi \tan \frac { d } { 8 }$ 
D)  $t = 2 \pi \arctan \frac { d } { 8 }$ 
A)  $t = \frac { 1 } { 2 \pi } \tan \frac { d } { 8 }$ 
B)  $t = \frac { 1 } { 2 \pi } \arctan \frac { d } { 8 }$ 
C)  $t = 2 \pi \tan \frac { d } { 8 }$ 
D)  $t = 2 \pi \arctan \frac { d } { 8 }$

Question 6

Use a calculator to evaluate the function. Round your answer to 4 decimal places.
-$\csc 0.1447$

Accepted Answer

A)  $0.1442$ 
B)  $0.9895$ 
C)  $1.0106$ 
D)  $6.9350$ 
A)  $0.1442$ 
B)  $0.9895$ 
C)  $1.0106$ 
D)  $6.9350$

Question 7

Evaluate without using a calculator by using ratios in a reference triangle.
-$\cos \left( - \frac { 5 \pi } { 4 } \right)$

Accepted Answer

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

Question 8

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
-y = -8sec x

Accepted Answer

A)  Reflection across the y-axis and horizontal stretch by a factor of 8 
B)  Reflection across the x-axis and vertical translation up 8 units 
C)  Reflection across the x-axis and vertical stretch by a factor of 8 
D)  Reflection across the x-axis and horizontal stretch by a factor of 8 
A)  Reflection across the y-axis and horizontal stretch by a factor of 8 
B)  Reflection across the x-axis and vertical translation up 8 units 
C)  Reflection across the x-axis and vertical stretch by a factor of 8 
D)  Reflection across the x-axis and horizontal stretch by a factor of 8

Question 9

Find the exact value of the real number y.
-$$y = \csc ^ { - 1 } ( - 2 )$$

Accepted Answer

A)  $\frac { \pi } { 6 }$ 
B)  $- \frac { \pi } { 3 }$ 
C)  $- \frac { \pi } { 6 }$ 
D)  $\frac { \pi } { 3 }$ 
A)  $\frac { \pi } { 6 }$ 
B)  $- \frac { \pi } { 3 }$ 
C)  $- \frac { \pi } { 6 }$ 
D)  $\frac { \pi } { 3 }$

Question 10

Find the angle in degrees that describes the compass bearing.
-ENE

Accepted Answer

A)  $67.5 ^ { \circ }$ 
B)  $22.5 ^ { \circ }$ 
C)  $90 ^ { \circ }$ 
D)  $45 ^ { \circ }$ 
A)  $67.5 ^ { \circ }$ 
B)  $22.5 ^ { \circ }$ 
C)  $90 ^ { \circ }$ 
D)  $45 ^ { \circ }$

Question 11

Choose the point on the terminal side of .
-$$\theta = \frac { - \pi } { 3 }$$

Accepted Answer

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

Question 12

Graph the function.
-$y=4 \cos x+\sin 4 x$

Accepted Answer

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

Question 13

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

Accepted Answer

A)  $\cot \theta = \frac { 3 \sqrt { 5 } } { 5 }$ 
B)  $\cot \theta = - \frac { \sqrt { 5 } } { 3 }$ 
C)  $\cot \theta = \frac { \sqrt { 70 } } { 5 }$ 
D)  $\cot \theta = \frac { 3 \sqrt { 14 } } { 14 }$ 
A)  $\cot \theta = \frac { 3 \sqrt { 5 } } { 5 }$ 
B)  $\cot \theta = - \frac { \sqrt { 5 } } { 3 }$ 
C)  $\cot \theta = \frac { \sqrt { 70 } } { 5 }$ 
D)  $\cot \theta = \frac { 3 \sqrt { 14 } } { 14 }$

Question 14

Solve the problem.
-From a distance of 1215 feet from a spotlight, the angle of elevation to a cloud base is 41°. Find the height of the cloud base to the nearest foot.

Accepted Answer

A)  797 feet 
B)  917 feet 
C)  1398 feet 
D)  1056 feet 
A)  797 feet 
B)  917 feet 
C)  1398 feet 
D)  1056 feet

Question 15

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined."
-$$\cos \frac { 17 \pi } { 2 }$$

Accepted Answer

A)  $- 1$ 
B)  1 
C)  0 
D)  undefined 
A)  $- 1$ 
B)  1 
C)  0 
D)  undefined

Question 16

Find the domain and range of the function.
-$$f ( x ) = 3 \sin | x |$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; range $[ - 3,3 ]$ 
B)  Domain: $( - \infty , \infty )$; range: $[ 0,3 ]$ 
C)  Domain: $[ - 3,3 ]$; range: $( - \infty , \infty )$ 
D)  Domain: $[ 0 , \infty )$; range: $[ 0,3 ]$ 
A)  Domain: $( - \infty , \infty )$; range $[ - 3,3 ]$ 
B)  Domain: $( - \infty , \infty )$; range: $[ 0,3 ]$ 
C)  Domain: $[ - 3,3 ]$; range: $( - \infty , \infty )$ 
D)  Domain: $[ 0 , \infty )$; range: $[ 0,3 ]$

Question 17

Use a calculator to graph the function.
-$$y = x ^ { 2 } \sin x$$

Accepted Answer

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

Question 18

Graph the function.
-$y=\cos \frac{4}{3} x$

Accepted Answer

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

Question 19

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
-$126 ^ { \circ }$

Accepted Answer

A)  $486 ^ { \circ } ; - 234 ^ { \circ }$ 
B)  $306 ^ { \circ } ; - 54 ^ { \circ }$ 
C)  $486 ^ { \circ } ; - 54 ^ { \circ }$ 
D)  $396 ^ { \circ } ; - 144 ^ { \circ }$ 
A)  $486 ^ { \circ } ; - 234 ^ { \circ }$ 
B)  $306 ^ { \circ } ; - 54 ^ { \circ }$ 
C)  $486 ^ { \circ } ; - 54 ^ { \circ }$ 
D)  $396 ^ { \circ } ; - 144 ^ { \circ }$

Question 20

Solve the problem.
-From a balloon 1122 feet high, the angle of depression to the ranger headquarters is $60 ^ { \circ } 13 ^ { \prime }$. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Accepted Answer

A)  $637 \mathrm { ft }$ 
B)  $647 \mathrm { ft }$ 
C)  $632 \mathrm { ft }$ 
D)  $642 \mathrm { ft }$ 
A)  $637 \mathrm { ft }$ 
B)  $647 \mathrm { ft }$ 
C)  $632 \mathrm { ft }$ 
D)  $642 \mathrm { ft }$

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - $\sin 1170 ^ { \circ }$

Evaluate without using a calculator. - $\cos \omega$ , if $\tan \omega = - \frac { 8 } { 5 }$ and $\sin \omega > 0$

Graph the expression $\sec ^ { 2 } x - \sec ^ { 2 } x \sin ^ { 2 } x$ on your calculator. Determine what constant or single circular function is equivalent to the given expression.

Evaluate without using a calculator by using ratios in a reference triangle. - $\sec 150 ^ { \circ }$

Solve. -A rotating beacon is located a distance $\mathrm { d }$ from a long wall. The distance $\mathrm { d }$ is given by $\mathrm { d } = 8$ tan $2 \pi \mathrm { t }$ , where $t$ is the time measured in seconds since the beacon started rotating. Solve the equation for $t$ .

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\csc 0.1447$

Evaluate without using a calculator by using ratios in a reference triangle. - $\cos \left( - \frac { 5 \pi } { 4 } \right)$

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. -y = -8sec x

Find the exact value of the real number y. - $y = \csc ^ { - 1 } ( - 2 )$

Find the angle in degrees that describes the compass bearing. -ENE

Choose the point on the terminal side of . - $\theta = \frac { - \pi } { 3 }$

Graph the function. - $y=4 \cos x+\sin 4 x$ $Graph the function. - y=4 \cos x+\sin 4 x$

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

Solve the problem. -From a distance of 1215 feet from a spotlight, the angle of elevation to a cloud base is 41°. Find the height of the cloud base to the nearest foot.

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - $\cos \frac { 17 \pi } { 2 }$

Find the domain and range of the function. - $f ( x ) = 3 \sin | x |$

Use a calculator to graph the function. - $y = x ^ { 2 } \sin x$ $Use a calculator to graph the function. - y = x ^ { 2 } \sin x$

Graph the function. - $y=\cos \frac{4}{3} x$ $Graph the function. - y=\cos \frac{4}{3} x$

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $126 ^ { \circ }$

Solve the problem. -From a balloon 1122 feet high, the angle of depression to the ranger headquarters is $60 ^ { \circ } 13 ^ { \prime }$ . How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

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

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - sin⁡1170∘\sin 1170 ^ { \circ }sin1170∘

Evaluate without using a calculator. - cos⁡ω\cos \omegacosω , if tan⁡ω=−85\tan \omega = - \frac { 8 } { 5 }tanω=−58​ and sin⁡ω>0\sin \omega > 0sinω>0

Graph the expression sec⁡2x−sec⁡2xsin⁡2x\sec ^ { 2 } x - \sec ^ { 2 } x \sin ^ { 2 } xsec2x−sec2xsin2x on your calculator. Determine what constant or single circular function is equivalent to the given expression.

Evaluate without using a calculator by using ratios in a reference triangle. - sec⁡150∘\sec 150 ^ { \circ }sec150∘

Solve. -A rotating beacon is located a distance d\mathrm { d }d from a long wall. The distance d\mathrm { d }d is given by d=8\mathrm { d } = 8d=8 tan 2πt2 \pi \mathrm { t }2πt , where ttt is the time measured in seconds since the beacon started rotating. Solve the equation for ttt .

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - csc⁡0.1447\csc 0.1447csc0.1447

Evaluate without using a calculator by using ratios in a reference triangle. - cos⁡(−5π4)\cos \left( - \frac { 5 \pi } { 4 } \right)cos(−45π​)

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. -y = -8sec x

Find the exact value of the real number y. - y=csc⁡−1(−2)y = \csc ^ { - 1 } ( - 2 )y=csc−1(−2)

Find the angle in degrees that describes the compass bearing. -ENE

Choose the point on the terminal side of . - θ=−π3\theta = \frac { - \pi } { 3 }θ=3−π​

Graph the function. - y=4cos⁡x+sin⁡4xy=4 \cos x+\sin 4 xy=4cosx+sin4x

Find the trigonometric function value for the angle shown. - cot⁡θ\cot \thetacotθ

Solve the problem. -From a distance of 1215 feet from a spotlight, the angle of elevation to a cloud base is 41°. Find the height of the cloud base to the nearest foot.

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - cos⁡17π2\cos \frac { 17 \pi } { 2 }cos217π​

Find the domain and range of the function. - f(x)=3sin⁡∣x∣f ( x ) = 3 \sin | x |f(x)=3sin∣x∣

Use a calculator to graph the function. - y=x2sin⁡xy = x ^ { 2 } \sin xy=x2sinx

Graph the function. - y=cos⁡43xy=\cos \frac{4}{3} xy=cos34​x

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - 126∘126 ^ { \circ }126∘

Solve the problem. -From a balloon 1122 feet high, the angle of depression to the ranger headquarters is 60∘13′60 ^ { \circ } 13 ^ { \prime }60∘13′ . How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

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

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - $\sin 1170 ^ { \circ }$

Evaluate without using a calculator. - $\cos \omega$ , if $\tan \omega = - \frac { 8 } { 5 }$ and $\sin \omega > 0$

Graph the expression $\sec ^ { 2 } x - \sec ^ { 2 } x \sin ^ { 2 } x$ on your calculator. Determine what constant or single circular function is equivalent to the given expression.

Evaluate without using a calculator by using ratios in a reference triangle. - $\sec 150 ^ { \circ }$

Solve. -A rotating beacon is located a distance $\mathrm { d }$ from a long wall. The distance $\mathrm { d }$ is given by $\mathrm { d } = 8$ tan $2 \pi \mathrm { t }$ , where $t$ is the time measured in seconds since the beacon started rotating. Solve the equation for $t$ .

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\csc 0.1447$

Evaluate without using a calculator by using ratios in a reference triangle. - $\cos \left( - \frac { 5 \pi } { 4 } \right)$

Find the exact value of the real number y. - $y = \csc ^ { - 1 } ( - 2 )$

Choose the point on the terminal side of . - $\theta = \frac { - \pi } { 3 }$

Graph the function. - $y=4 \cos x+\sin 4 x$ $Graph the function. - y=4 \cos x+\sin 4 x$

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

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - $\cos \frac { 17 \pi } { 2 }$

Find the domain and range of the function. - $f ( x ) = 3 \sin | x |$

Use a calculator to graph the function. - $y = x ^ { 2 } \sin x$ $Use a calculator to graph the function. - y = x ^ { 2 } \sin x$

Graph the function. - $y=\cos \frac{4}{3} x$ $Graph the function. - y=\cos \frac{4}{3} x$

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $126 ^ { \circ }$

Solve the problem. -From a balloon 1122 feet high, the angle of depression to the ranger headquarters is $60 ^ { \circ } 13 ^ { \prime }$ . How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?