Question 1

Determine the exact value, if it exists, of $\sec ( - \pi )$.

Accepted Answer

A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $- 1$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  1 
E)  The value does not exist. 
A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $- 1$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  1 
E)  The value does not exist.

Question 2

Evaluate, if possible, the given trigonometric function at the indicated value.
$$\sec t , t = \frac { 5 \pi } { 6 }$$

Accepted Answer

A)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
B)  2 
C)  -2 
D)  $- \frac { \sqrt { 3 } } { 2 }$ 
E)  not possible 
A)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
B)  2 
C)  -2 
D)  $- \frac { \sqrt { 3 } } { 2 }$ 
E)  not possible

Question 3

Rewrite the angle $\frac { \pi } { 6 }$ radians in degree measure.

Accepted Answer

A)  $60 ^ { \circ }$ 
B)  $20 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $15 ^ { \circ }$ 
E)  $330 ^ { \circ }$ 
A)  $60 ^ { \circ }$ 
B)  $20 ^ { \circ }$ 
C)  $30 ^ { \circ }$ 
D)  $15 ^ { \circ }$ 
E)  $330 ^ { \circ }$

Question 4

Approximate $\sin ^ { - 1 } ( - 0.51 )$. Round your answer to four decimal places.

Accepted Answer

A)  $- 1.8685$ 
B)  $- 2.0484$ 
C)  $- 0.4882$ 
D)  $- 0.5352$ 
E)  $- 0.9249$ 
A)  $- 1.8685$ 
B)  $- 2.0484$ 
C)  $- 0.4882$ 
D)  $- 0.5352$ 
E)  $- 0.9249$

Question 5

Find (if possible) the complement and supplement of the given angle. $51 ^ { \circ }$

Accepted Answer

A)  complement: $129 ^ { \circ }$; supplement: $39 ^ { \circ }$ 
B)  complement: $51 ^ { \circ }$; supplement: $129 ^ { \circ }$ 
C)  complement : $129 ^ { \circ }$; supplement: $309 ^ { \circ }$ 
D)  complement: $39 ^ { \circ }$; supplement: $309 ^ { \circ }$ 
E)  complement: $39 ^ { \circ }$; supplement: $129 ^ { \circ }$ 
A)  complement: $129 ^ { \circ }$; supplement: $39 ^ { \circ }$ 
B)  complement: $51 ^ { \circ }$; supplement: $129 ^ { \circ }$ 
C)  complement : $129 ^ { \circ }$; supplement: $309 ^ { \circ }$ 
D)  complement: $39 ^ { \circ }$; supplement: $309 ^ { \circ }$ 
E)  complement: $39 ^ { \circ }$; supplement: $129 ^ { \circ }$

Question 6

Find the exact value of the given trigonometric function of the angle $\theta$ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: $\cos \theta$

Accepted Answer

A)  $\frac { 8 } { 17 }$ 
B)  $\frac { 15 } { 17 }$ 
C)  $\frac { 8 } { 15 }$ 
D)  $\frac { 15 } { 8 }$ 
E)  $\frac { 17 } { 15 }$ 
A)  $\frac { 8 } { 17 }$ 
B)  $\frac { 15 } { 17 }$ 
C)  $\frac { 8 } { 15 }$ 
D)  $\frac { 15 } { 8 }$ 
E)  $\frac { 17 } { 15 }$

Question 7

$\text { Determine the graph of } y=5 \sin (x)$

Accepted Answer

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

Question 8

Given that $\cos \theta = \frac { 14 } { 15 }$, find $\csc \theta$.
(Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$; then use the Pythagorean Theorem to determine the third side.)

Accepted Answer

A)  $\frac { \sqrt { 29 } } { 15 }$ 
B)  $\frac { 15 } { 14 }$ 
C)  $\frac { 14 } { \sqrt { 29 } }$ 
D)  $15 \sqrt { 29 }$ 
E)  $\frac { 15 } { \sqrt { 29 } }$ 
A)  $\frac { \sqrt { 29 } } { 15 }$ 
B)  $\frac { 15 } { 14 }$ 
C)  $\frac { 14 } { \sqrt { 29 } }$ 
D)  $15 \sqrt { 29 }$ 
E)  $\frac { 15 } { \sqrt { 29 } }$

Question 9

Use the properties of inverse trigonometric functions to evaluate $\arcsin \left[ \sin \left( \frac { 4 \pi } { 9 } \right) \right]$.

Accepted Answer

A)  $- \frac { 5 \pi } { 9 }$ 
B)  $\frac { 4 \pi } { 5 }$ 
C)  $\frac { 9 \pi } { 4 }$ 
D)  $\frac { 4 \pi } { 9 }$ 
E)  $\frac { \pi } { 9 }$ 
A)  $- \frac { 5 \pi } { 9 }$ 
B)  $\frac { 4 \pi } { 5 }$ 
C)  $\frac { 9 \pi } { 4 }$ 
D)  $\frac { 4 \pi } { 9 }$ 
E)  $\frac { \pi } { 9 }$

Question 10

Use a calculator to evaluate $\cot \left( \frac { \pi } { 6 } \right)$. Round your answer to four decimal places.

Accepted Answer

A)  $1.7321$ 
B)  $0.5773$ 
C)  $- 0.1561$ 
D)  $- 6.4061$ 
E)  $5.9443$ 
A)  $1.7321$ 
B)  $0.5773$ 
C)  $- 0.1561$ 
D)  $- 6.4061$ 
E)  $5.9443$

Question 11

When an airplane leaves the runway, its angle of climb is $15 ^ { \circ }$ and its speed is 275 feet per second. Find the plane's altitude relative to the runway in feet after 1 minute. Round your answer to the nearest foot.

Accepted Answer

A)  $3417 \mathrm { feet }$ 
B)  2563 feet 
C)  $5979 \mathrm { feet }$ 
D)  $4271 \mathrm { feet }$ 
E)  5125 feet 
A)  $3417 \mathrm { feet }$ 
B)  2563 feet 
C)  $5979 \mathrm { feet }$ 
D)  $4271 \mathrm { feet }$ 
E)  5125 feet

Question 12

Find the exact value of $\sec \left( \arctan \frac { 8 } { 15 } \right)$.

Accepted Answer

A)  $\frac { 8 } { 15 }$ 
B)  $\frac { 32 } { 15 }$ 
C)  $\frac { 17 } { 15 }$ 
D)  $\frac { 17 } { 32 }$ 
E)  $\frac { 15 } { 8 }$ 
A)  $\frac { 8 } { 15 }$ 
B)  $\frac { 32 } { 15 }$ 
C)  $\frac { 17 } { 15 }$ 
D)  $\frac { 17 } { 32 }$ 
E)  $\frac { 15 } { 8 }$

Question 13

Use trigonometric identities to transform the left side of the equation into the right side. Assume all angles are positive acute angles, and show all of your work.
$$( \csc x - \cot x ) ( \csc x + \cot x ) = 1$$

Accepted Answer

\[\begin{aligned}
( \csc x - \cot x ) (

Question 14

Determine the exact value of $\csc \theta$ when $\cos \theta = \frac { 5 } { 13 }$ and $\cot \theta < 0$.

Accepted Answer

A)  $\csc \theta = - \frac { 1 } { 12 }$ 
B)  $\csc \theta = - \frac { 13 } { 12 }$ 
C)  $\csc \theta = - \frac { 12 } { 13 }$ 
D)  $\csc \theta = - \frac { 13 } { 6 }$ 
E)  $\csc \theta = - \frac { 14 } { 11 }$ 
A)  $\csc \theta = - \frac { 1 } { 12 }$ 
B)  $\csc \theta = - \frac { 13 } { 12 }$ 
C)  $\csc \theta = - \frac { 12 } { 13 }$ 
D)  $\csc \theta = - \frac { 13 } { 6 }$ 
E)  $\csc \theta = - \frac { 14 } { 11 }$

Question 15

Convert the given angle measure from degrees to radians. Round to three decimal places.
$- 365.9 ^ { \circ }$

Accepted Answer

A)  $- 6.386$ 
B)  $- 5.863$ 
C)  $- 20964.526$ 
D)  $- 3.193$ 
E)  $- 12.772$ 
A)  $- 6.386$ 
B)  $- 5.863$ 
C)  $- 20964.526$ 
D)  $- 3.193$ 
E)  $- 12.772$

Question 16

Evaluate $\sec ( 4.9 )$. Round your answer to four decimal places.

Accepted Answer

A)  $- 1.0179$ 
B)  $0.1865$ 
C)  $- 0.9825$ 
D)  $5.3616$ 
E)  $0.9792$ 
A)  $- 1.0179$ 
B)  $0.1865$ 
C)  $- 0.9825$ 
D)  $5.3616$ 
E)  $0.9792$

Question 17

Use a graphing utility to graph the function below, making sure to show at least two periods.
$\sec \frac { x } { 2 }$

Accepted Answer

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

Question 18

The point $( - 8 , - 15 )$ is on the terminal side of an angle in standard position. Determine the exact value of $\sin \theta$.

Accepted Answer

A)  $\sin \theta = - \frac { 8 } { 17 }$ 
B)  $\sin \theta = - \frac { 9 } { 8 }$ 
C)  $\sin \theta = - \frac { 15 } { 17 }$ 
D)  $\sin \theta = - \frac { 2 } { 15 }$ 
E)  $\sin \theta = - \frac { 17 } { 8 }$ 
A)  $\sin \theta = - \frac { 8 } { 17 }$ 
B)  $\sin \theta = - \frac { 9 } { 8 }$ 
C)  $\sin \theta = - \frac { 15 } { 17 }$ 
D)  $\sin \theta = - \frac { 2 } { 15 }$ 
E)  $\sin \theta = - \frac { 17 } { 8 }$

Question 19

Determine the exact value of $\arcsin ( - 0.5 )$.

Accepted Answer

A)  $\frac { \pi } { 6 }$ 
B)  0 
C)  $- \frac { \pi } { 6 }$ 
D)  $\frac { \pi } { 3 }$ 
E)  $- \frac { \pi } { 3 }$ 
A)  $\frac { \pi } { 6 }$ 
B)  0 
C)  $- \frac { \pi } { 6 }$ 
D)  $\frac { \pi } { 3 }$ 
E)  $- \frac { \pi } { 3 }$

Question 20

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $\tan 1.7$

Accepted Answer

A)  $0.0297$ 
B)  $0.9917$ 
C)  $- 0.1288$ 
D)  $- 7.6966$ 
E)  $1.0084$ 
A)  $0.0297$ 
B)  $0.9917$ 
C)  $- 0.1288$ 
D)  $- 7.6966$ 
E)  $1.0084$

Determine the exact value, if it exists, of $\sec ( - \pi )$ .

Evaluate, if possible, the given trigonometric function at the indicated value. $\sec t , t = \frac { 5 \pi } { 6 }$

Rewrite the angle $\frac { \pi } { 6 }$ radians in degree measure.

Approximate $\sin ^ { - 1 } ( - 0.51 )$ . Round your answer to four decimal places.

Find (if possible) the complement and supplement of the given angle. $51 ^ { \circ }$

$\text { Determine the graph of } y=5 \sin (x)$

Given that $\cos \theta = \frac { 14 } { 15 }$ , find $\csc \theta$ . (Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$ ; then use the Pythagorean Theorem to determine the third side.)

Use the properties of inverse trigonometric functions to evaluate $\arcsin \left[ \sin \left( \frac { 4 \pi } { 9 } \right) \right]$ .

Use a calculator to evaluate $\cot \left( \frac { \pi } { 6 } \right)$ . Round your answer to four decimal places.

When an airplane leaves the runway, its angle of climb is $15 ^ { \circ }$ and its speed is 275 feet per second. Find the plane's altitude relative to the runway in feet after 1 minute. Round your answer to the nearest foot.

Find the exact value of $\sec \left( \arctan \frac { 8 } { 15 } \right)$ .

Use trigonometric identities to transform the left side of the equation into the right side. Assume all angles are positive acute angles, and show all of your work. $( \csc x - \cot x ) ( \csc x + \cot x ) = 1$

Determine the exact value of $\csc \theta$ when $\cos \theta = \frac { 5 } { 13 }$ and $\cot \theta < 0$ .

Convert the given angle measure from degrees to radians. Round to three decimal places. $- 365.9 ^ { \circ }$

Evaluate $\sec ( 4.9 )$ . Round your answer to four decimal places.

Use a graphing utility to graph the function below, making sure to show at least two periods. $\sec \frac { x } { 2 }$

The point $( - 8 , - 15 )$ is on the terminal side of an angle in standard position. Determine the exact value of $\sin \theta$ .

Determine the exact value of $\arcsin ( - 0.5 )$ .

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $\tan 1.7$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Exam 4: Trigonometric Functions

Determine the exact value, if it exists, of sec⁡(−π)\sec ( - \pi )sec(−π) .

Evaluate, if possible, the given trigonometric function at the indicated value. sec⁡t,t=5π6\sec t , t = \frac { 5 \pi } { 6 }sect,t=65π​

Rewrite the angle π6\frac { \pi } { 6 }6π​ radians in degree measure.

Approximate sin⁡−1(−0.51)\sin ^ { - 1 } ( - 0.51 )sin−1(−0.51) . Round your answer to four decimal places.

Find (if possible) the complement and supplement of the given angle. 51∘51 ^ { \circ }51∘

Find the exact value of the given trigonometric function of the angle θ\thetaθ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: cos⁡θ\cos \thetacosθ

Determine the graph of y=5sin⁡(x)\text { Determine the graph of } y=5 \sin (x) Determine the graph of y=5sin(x)

Given that cos⁡θ=1415\cos \theta = \frac { 14 } { 15 }cosθ=1514​ , find csc⁡θ\csc \thetacscθ . (Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle θ\thetaθ ; then use the Pythagorean Theorem to determine the third side.)

Use the properties of inverse trigonometric functions to evaluate arcsin⁡[sin⁡(4π9)]\arcsin \left[ \sin \left( \frac { 4 \pi } { 9 } \right) \right]arcsin[sin(94π​)] .

Use a calculator to evaluate cot⁡(π6)\cot \left( \frac { \pi } { 6 } \right)cot(6π​) . Round your answer to four decimal places.

When an airplane leaves the runway, its angle of climb is 15∘15 ^ { \circ }15∘ and its speed is 275 feet per second. Find the plane's altitude relative to the runway in feet after 1 minute. Round your answer to the nearest foot.

Find the exact value of sec⁡(arctan⁡815)\sec \left( \arctan \frac { 8 } { 15 } \right)sec(arctan158​) .

Use trigonometric identities to transform the left side of the equation into the right side. Assume all angles are positive acute angles, and show all of your work. (csc⁡x−cot⁡x)(csc⁡x+cot⁡x)=1( \csc x - \cot x ) ( \csc x + \cot x ) = 1(cscx−cotx)(cscx+cotx)=1

Determine the exact value of csc⁡θ\csc \thetacscθ when cos⁡θ=513\cos \theta = \frac { 5 } { 13 }cosθ=135​ and cot⁡θ<0\cot \theta < 0cotθ<0 .

Convert the given angle measure from degrees to radians. Round to three decimal places. −365.9∘- 365.9 ^ { \circ }−365.9∘

Evaluate sec⁡(4.9)\sec ( 4.9 )sec(4.9) . Round your answer to four decimal places.

Use a graphing utility to graph the function below, making sure to show at least two periods. sec⁡x2\sec \frac { x } { 2 }sec2x​

The point (−8,−15)( - 8 , - 15 )(−8,−15) is on the terminal side of an angle in standard position. Determine the exact value of sin⁡θ\sin \thetasinθ .

Determine the exact value of arcsin⁡(−0.5)\arcsin ( - 0.5 )arcsin(−0.5) .

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) tan⁡1.7\tan 1.7tan1.7

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Determine the exact value, if it exists, of $\sec ( - \pi )$ .

Evaluate, if possible, the given trigonometric function at the indicated value. $\sec t , t = \frac { 5 \pi } { 6 }$

Rewrite the angle $\frac { \pi } { 6 }$ radians in degree measure.

Approximate $\sin ^ { - 1 } ( - 0.51 )$ . Round your answer to four decimal places.

Find (if possible) the complement and supplement of the given angle. $51 ^ { \circ }$

$\text { Determine the graph of } y=5 \sin (x)$

Given that $\cos \theta = \frac { 14 } { 15 }$ , find $\csc \theta$ . (Hint: Sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$ ; then use the Pythagorean Theorem to determine the third side.)

Use the properties of inverse trigonometric functions to evaluate $\arcsin \left[ \sin \left( \frac { 4 \pi } { 9 } \right) \right]$ .

Use a calculator to evaluate $\cot \left( \frac { \pi } { 6 } \right)$ . Round your answer to four decimal places.

When an airplane leaves the runway, its angle of climb is $15 ^ { \circ }$ and its speed is 275 feet per second. Find the plane's altitude relative to the runway in feet after 1 minute. Round your answer to the nearest foot.

Find the exact value of $\sec \left( \arctan \frac { 8 } { 15 } \right)$ .

Use trigonometric identities to transform the left side of the equation into the right side. Assume all angles are positive acute angles, and show all of your work. $( \csc x - \cot x ) ( \csc x + \cot x ) = 1$

Determine the exact value of $\csc \theta$ when $\cos \theta = \frac { 5 } { 13 }$ and $\cot \theta < 0$ .

Convert the given angle measure from degrees to radians. Round to three decimal places. $- 365.9 ^ { \circ }$

Evaluate $\sec ( 4.9 )$ . Round your answer to four decimal places.

Use a graphing utility to graph the function below, making sure to show at least two periods. $\sec \frac { x } { 2 }$

The point $( - 8 , - 15 )$ is on the terminal side of an angle in standard position. Determine the exact value of $\sin \theta$ .

Determine the exact value of $\arcsin ( - 0.5 )$ .

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is set in the correct angle mode.) $\tan 1.7$