Question 1

Approximate $\tan ^ { - 1 } ( 3 )$. Round your answer to four decimal places.

Accepted Answer

A)  $1.2490$ 
B)  $0.3463$ 
C)  $- 0.1425$ 
D)  $0.8006$ 
E)  $- 7.0153$ 
A)  $1.2490$ 
B)  $0.3463$ 
C)  $- 0.1425$ 
D)  $0.8006$ 
E)  $- 7.0153$

Question 2

Evaluate, if possible, the given trigonometric function at the indicated value.
$$\sin t , t = \frac { 4 \pi } { 3 }$$

Accepted Answer

A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
D)  $\frac { \sqrt { 3 } } { 2 }$ 
E)  not possible 
A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
D)  $\frac { \sqrt { 3 } } { 2 }$ 
E)  not possible

Question 3

A communications company erects a 91-foot tall cellular telephone tower on level ground. Determine the angle of depression, $\theta$ (in degrees), from the top of the tower to a point 55 feet from the base of the tower. Round answer to two decimal places.

Accepted Answer

A)  $41.85 ^ { \circ }$ 
B)  $50.35 ^ { \circ }$ 
C)  $58.85 ^ { \circ }$ 
D)  $30.73 ^ { \circ }$ 
E)  $55.73 ^ { \circ }$ 
A)  $41.85 ^ { \circ }$ 
B)  $50.35 ^ { \circ }$ 
C)  $58.85 ^ { \circ }$ 
D)  $30.73 ^ { \circ }$ 
E)  $55.73 ^ { \circ }$

Question 4

The circular blade of a saw has a diameter of 8 inches and rotates at 2000 revolutions per minute. Find the linear speed of the saw teeth in feet per second. Round your answer to two decimal places.

Accepted Answer

A)  $139.63$ feet per second 
B)  $837.76$ feet per second 
C)  $11.11$ feet per second 
D)  $69.81$ feet per second 
E)  $209.44$ feet per second 
A)  $139.63$ feet per second 
B)  $837.76$ feet per second 
C)  $11.11$ feet per second 
D)  $69.81$ feet per second 
E)  $209.44$ feet per second

Question 5

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.)
$\csc 57 ^ { \circ } 27 ^ { \prime }$

Accepted Answer

A)  $0.8429$ 
B)  $1.2753$ 
C)  $1.1863$ 
D)  $1.8586$ 
E)  $- 1.4725$ 
A)  $0.8429$ 
B)  $1.2753$ 
C)  $1.1863$ 
D)  $1.8586$ 
E)  $- 1.4725$

Question 6

The point $( - 3 , - 4 )$ is on the terminal side of an angle in standard position. Determine the exact value of $\sin \theta$.

Accepted Answer

A)  $\sin \theta = - \frac { 3 } { 5 }$ 
B)  $\sin \theta = - \frac { 2 } { 3 }$ 
C)  $\sin \theta = - \frac { 4 } { 5 }$ 
D)  $\sin \theta = - \frac { 1 } { 4 }$ 
E)  $\quad \sin \theta = - \frac { 5 } { 3 }$ 
A)  $\sin \theta = - \frac { 3 } { 5 }$ 
B)  $\sin \theta = - \frac { 2 } { 3 }$ 
C)  $\sin \theta = - \frac { 4 } { 5 }$ 
D)  $\sin \theta = - \frac { 1 } { 4 }$ 
E)  $\quad \sin \theta = - \frac { 5 } { 3 }$

Question 7

Evaluate the trigonometric function using its period as an aid.
$$\sin \left( \frac { 13 \pi } { 3 } \right)$$

Accepted Answer

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

Question 8

Determine the quadrant in which the angle $- 281.2 ^ { \circ }$ lies.

Accepted Answer

A)  Quadrant II 
B)  Quadrant I 
C)  Quadrant III 
D)  Quadrant IV 
A)  Quadrant II 
B)  Quadrant I 
C)  Quadrant III 
D)  Quadrant IV

Question 9

Determine a pair of angles (one positive and one negative) in degree measure coterminal to the angle $117 ^ { \circ }$.

Accepted Answer

A)  $297 ^ { \circ } , - 63 ^ { \circ }$ 
B)  $477 ^ { \circ } , - 243 ^ { \circ }$ 
C)  $417 ^ { \circ } , - 183 ^ { \circ }$ 
D)  $234 ^ { \circ } , - 117 ^ { \circ }$ 
E)  $297 ^ { \circ } , - 243 ^ { \circ }$ 
A)  $297 ^ { \circ } , - 63 ^ { \circ }$ 
B)  $477 ^ { \circ } , - 243 ^ { \circ }$ 
C)  $417 ^ { \circ } , - 183 ^ { \circ }$ 
D)  $234 ^ { \circ } , - 117 ^ { \circ }$ 
E)  $297 ^ { \circ } , - 243 ^ { \circ }$

Question 10

Find the point $( x , y )$ on the unit circle corresponding to the real number $t = - \frac { \pi } { 6 }$.

Accepted Answer

A)  $\left( - \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ 
C)  $\left( - \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ 
D)  $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ 
E)  $\left( \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right)$ 
A)  $\left( - \frac { 1 } { 2 } , \frac { \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( \frac { \sqrt { 3 } } { 2 } , - \frac { 1 } { 2 } \right)$ 
C)  $\left( - \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ 
D)  $\left( \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } \right)$ 
E)  $\left( \frac { \sqrt { 2 } } { 2 } , \frac { \sqrt { 2 } } { 2 } \right)$

Question 11

Determine the exact value of the tangent of the quadrant angle $\frac { 3 \pi } { 2 }$.

Accepted Answer

A)  undefined 
B)  0 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { \sqrt { 2 } } { 2 }$ 
E)  $\frac { 1 } { 2 }$ 
A)  undefined 
B)  0 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { \sqrt { 2 } } { 2 }$ 
E)  $\frac { 1 } { 2 }$

Question 12

Determine the quadrant in which the angle $- 191 ^ { \circ }$ lies.

Accepted Answer

A)  Quadrant III 
B)  Quadrant II 
C)  Quadrant IV 
D)  Quadrant I 
A)  Quadrant III 
B)  Quadrant II 
C)  Quadrant IV 
D)  Quadrant I

Question 13

Find the amplitude of $y = - \frac { \pi } { 7 } \cos \left( \frac { 3 x } { 2 } \right)$.

Accepted Answer

A)  $- \frac { \pi } { 7 }$ 
B)  $\frac { 4 \pi } { 3 }$ 
C)  $\frac { 3 } { 2 }$ 
D)  $\frac { 1 } { 7 }$ 
E)  $\frac { \pi } { 7 }$ 
A)  $- \frac { \pi } { 7 }$ 
B)  $\frac { 4 \pi } { 3 }$ 
C)  $\frac { 3 } { 2 }$ 
D)  $\frac { 1 } { 7 }$ 
E)  $\frac { \pi } { 7 }$

Question 14

Find the cotangent (if it exists) of the real number $t = - \frac { 5 \pi } { 4 }$.

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $- 1$ 
C)  1 
D)  0 
E)  $\cot \left( - \frac { 5 \pi } { 4 } \right)$ does not exist 
A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $- 1$ 
C)  1 
D)  0 
E)  $\cot \left( - \frac { 5 \pi } { 4 } \right)$ does not exist

Question 15

Evaluate the cosine of the angle without using a calculator.
$330 ^ { \circ }$

Accepted Answer

A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $- \frac { \sqrt { 2 } } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 2 }$ 
E)  0 
A)  $\frac { \sqrt { 2 } } { 2 }$ 
B)  $- \frac { \sqrt { 2 } } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 2 }$ 
E)  0

Question 16

State the quadrant in which $\theta$ lies. $\cot ( \theta )  0$

Accepted Answer

A)  Quadrant III 
B)  Quadrant I 
C)  Quadrant IV 
D)  Quadrant II 
E)  Quadrant I or Quadrant III 
A)  Quadrant III 
B)  Quadrant I 
C)  Quadrant IV 
D)  Quadrant II 
E)  Quadrant I or Quadrant III

Question 17

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.)
$\cot 53 ^ { \circ } 30 ^ { \prime }$

Accepted Answer

A)  $1.3514$ 
B)  $10.7304$ 
C)  $0.7400$ 
D)  $- 1.1859$ 
E)  $- 0.8433$ 
A)  $1.3514$ 
B)  $10.7304$ 
C)  $0.7400$ 
D)  $- 1.1859$ 
E)  $- 0.8433$

Question 18

State the quadrant in which $\theta$ lies if $\sec \theta < 0$ and $\tan \theta < 0$.

Accepted Answer

A)  Quadrant III 
B)  Quadrant IV 
C)  Quadrant I 
D)  Quadrant II 
A)  Quadrant III 
B)  Quadrant IV 
C)  Quadrant I 
D)  Quadrant II

Question 19

Find the radius of a circular sector with an arc length 26 feet and a central angle $\frac { 3 \pi } { 2 }$ radians. Round your answer to two decimal places.

Accepted Answer

A)  $5.52 \mathrm { feet }$ 
B)  $12.41$ feet 
C)  $3.40$ feet 
D)  $0.18$ foot 
E)  $0.08$ foot 
A)  $5.52 \mathrm { feet }$ 
B)  $12.41$ feet 
C)  $3.40$ feet 
D)  $0.18$ foot 
E)  $0.08$ foot

Question 20

Determine the exact value of $\csc \theta$ when $\cos \theta = \frac { 11 } { 61 }$ and $\sin \theta < 0$.

Accepted Answer

A)  $\csc \theta = - \frac { 1 } { 60 }$ 
B)  $\csc \theta = - \frac { 61 } { 60 }$ 
C)  $\csc \theta = - \frac { 60 } { 61 }$ 
D)  $\csc \theta = - \frac { 61 } { 30 }$ 
E)  $\csc \theta = - \frac { 62 } { 59 }$ 
A)  $\csc \theta = - \frac { 1 } { 60 }$ 
B)  $\csc \theta = - \frac { 61 } { 60 }$ 
C)  $\csc \theta = - \frac { 60 } { 61 }$ 
D)  $\csc \theta = - \frac { 61 } { 30 }$ 
E)  $\csc \theta = - \frac { 62 } { 59 }$

Approximate $\tan ^ { - 1 } ( 3 )$ . Round your answer to four decimal places.

Evaluate, if possible, the given trigonometric function at the indicated value. $\sin t , t = \frac { 4 \pi } { 3 }$

A communications company erects a 91-foot tall cellular telephone tower on level ground. Determine the angle of depression, $\theta$ (in degrees), from the top of the tower to a point 55 feet from the base of the tower. Round answer to two decimal places.

The circular blade of a saw has a diameter of 8 inches and rotates at 2000 revolutions per minute. Find the linear speed of the saw teeth in feet per second. Round your answer to two decimal places.

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) $\csc 57 ^ { \circ } 27 ^ { \prime }$

The point $( - 3 , - 4 )$ is on the terminal side of an angle in standard position. Determine the exact value of $\sin \theta$ .

Evaluate the trigonometric function using its period as an aid. $\sin \left( \frac { 13 \pi } { 3 } \right)$

Determine the quadrant in which the angle $- 281.2 ^ { \circ }$ lies.

Determine a pair of angles (one positive and one negative) in degree measure coterminal to the angle $117 ^ { \circ }$ .

Find the point $( x , y )$ on the unit circle corresponding to the real number $t = - \frac { \pi } { 6 }$ .

Determine the exact value of the tangent of the quadrant angle $\frac { 3 \pi } { 2 }$ .

Determine the quadrant in which the angle $- 191 ^ { \circ }$ lies.

Find the amplitude of $y = - \frac { \pi } { 7 } \cos \left( \frac { 3 x } { 2 } \right)$ .

Find the cotangent (if it exists) of the real number $t = - \frac { 5 \pi } { 4 }$ .

Evaluate the cosine of the angle without using a calculator. $330 ^ { \circ }$

State the quadrant in which $\theta$ lies. $\cot ( \theta ) < 0$ and $\sec ( \theta ) > 0$

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) $\cot 53 ^ { \circ } 30 ^ { \prime }$

State the quadrant in which $\theta$ lies if $\sec \theta < 0$ and $\tan \theta < 0$ .

Find the radius of a circular sector with an arc length 26 feet and a central angle $\frac { 3 \pi } { 2 }$ radians. Round your answer to two decimal places.

Determine the exact value of $\csc \theta$ when $\cos \theta = \frac { 11 } { 61 }$ and $\sin \theta < 0$ .

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

Approximate tan⁡−1(3)\tan ^ { - 1 } ( 3 )tan−1(3) . Round your answer to four decimal places.

Evaluate, if possible, the given trigonometric function at the indicated value. sin⁡t,t=4π3\sin t , t = \frac { 4 \pi } { 3 }sint,t=34π​

A communications company erects a 91-foot tall cellular telephone tower on level ground. Determine the angle of depression, θ\thetaθ (in degrees), from the top of the tower to a point 55 feet from the base of the tower. Round answer to two decimal places.

The circular blade of a saw has a diameter of 8 inches and rotates at 2000 revolutions per minute. Find the linear speed of the saw teeth in feet per second. Round your answer to two decimal places.

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) csc⁡57∘27′\csc 57 ^ { \circ } 27 ^ { \prime }csc57∘27′

The point (−3,−4)( - 3 , - 4 )(−3,−4) is on the terminal side of an angle in standard position. Determine the exact value of sin⁡θ\sin \thetasinθ .

Evaluate the trigonometric function using its period as an aid. sin⁡(13π3)\sin \left( \frac { 13 \pi } { 3 } \right)sin(313π​)

Determine the quadrant in which the angle −281.2∘- 281.2 ^ { \circ }−281.2∘ lies.

Determine a pair of angles (one positive and one negative) in degree measure coterminal to the angle 117∘117 ^ { \circ }117∘ .

Find the point (x,y)( x , y )(x,y) on the unit circle corresponding to the real number t=−π6t = - \frac { \pi } { 6 }t=−6π​ .

Determine the exact value of the tangent of the quadrant angle 3π2\frac { 3 \pi } { 2 }23π​ .

Determine the quadrant in which the angle −191∘- 191 ^ { \circ }−191∘ lies.

Find the amplitude of y=−π7cos⁡(3x2)y = - \frac { \pi } { 7 } \cos \left( \frac { 3 x } { 2 } \right)y=−7π​cos(23x​) .

Find the cotangent (if it exists) of the real number t=−5π4t = - \frac { 5 \pi } { 4 }t=−45π​ .

Evaluate the cosine of the angle without using a calculator. 330∘330 ^ { \circ }330∘

State the quadrant in which θ\thetaθ lies. cot⁡(θ)<0\cot ( \theta ) < 0cot(θ)<0 and sec⁡(θ)>0\sec ( \theta ) > 0sec(θ)>0

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) cot⁡53∘30′\cot 53 ^ { \circ } 30 ^ { \prime }cot53∘30′

State the quadrant in which θ\thetaθ lies if sec⁡θ<0\sec \theta < 0secθ<0 and tan⁡θ<0\tan \theta < 0tanθ<0 .

Find the radius of a circular sector with an arc length 26 feet and a central angle 3π2\frac { 3 \pi } { 2 }23π​ radians. Round your answer to two decimal places.

Determine the exact value of csc⁡θ\csc \thetacscθ when cos⁡θ=1161\cos \theta = \frac { 11 } { 61 }cosθ=6111​ and sin⁡θ<0\sin \theta < 0sinθ<0 .

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

Approximate $\tan ^ { - 1 } ( 3 )$ . Round your answer to four decimal places.

Evaluate, if possible, the given trigonometric function at the indicated value. $\sin t , t = \frac { 4 \pi } { 3 }$

A communications company erects a 91-foot tall cellular telephone tower on level ground. Determine the angle of depression, $\theta$ (in degrees), from the top of the tower to a point 55 feet from the base of the tower. Round answer to two decimal places.

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) $\csc 57 ^ { \circ } 27 ^ { \prime }$

The point $( - 3 , - 4 )$ is on the terminal side of an angle in standard position. Determine the exact value of $\sin \theta$ .

Evaluate the trigonometric function using its period as an aid. $\sin \left( \frac { 13 \pi } { 3 } \right)$

Determine the quadrant in which the angle $- 281.2 ^ { \circ }$ lies.

Determine a pair of angles (one positive and one negative) in degree measure coterminal to the angle $117 ^ { \circ }$ .

Find the point $( x , y )$ on the unit circle corresponding to the real number $t = - \frac { \pi } { 6 }$ .

Determine the exact value of the tangent of the quadrant angle $\frac { 3 \pi } { 2 }$ .

Determine the quadrant in which the angle $- 191 ^ { \circ }$ lies.

Find the amplitude of $y = - \frac { \pi } { 7 } \cos \left( \frac { 3 x } { 2 } \right)$ .

Find the cotangent (if it exists) of the real number $t = - \frac { 5 \pi } { 4 }$ .

Evaluate the cosine of the angle without using a calculator. $330 ^ { \circ }$

State the quadrant in which $\theta$ lies. $\cot ( \theta ) < 0$ and $\sec ( \theta ) > 0$

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) $\cot 53 ^ { \circ } 30 ^ { \prime }$

State the quadrant in which $\theta$ lies if $\sec \theta < 0$ and $\tan \theta < 0$ .

Find the radius of a circular sector with an arc length 26 feet and a central angle $\frac { 3 \pi } { 2 }$ radians. Round your answer to two decimal places.

Determine the exact value of $\csc \theta$ when $\cos \theta = \frac { 11 } { 61 }$ and $\sin \theta < 0$ .