Question 1

Determine the graph of $y = \cos \left( \frac { 5 x } { 3 } \right)$.

Accepted Answer

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

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 A

Question 3

The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the line.
$\begin{array} { c c l } \text { Line } & \text { Quadrant } & \text { Evaluate: } \ y = 10 x & \text { I } & \cos \theta \end{array}$

Accepted Answer

A)  $\sqrt { 101 }$ 
B)  $\frac { 1 } { \sqrt { 101 } }$ 
C)  $\frac { 1 } { 10 }$ 
D)  $\frac { 10 } { \sqrt { 101 } }$ 
E)  $- \frac { 10 } { \sqrt { 101 } }$ 
A)  $\sqrt { 101 }$ 
B)  $\frac { 1 } { \sqrt { 101 } }$ 
C)  $\frac { 1 } { 10 }$ 
D)  $\frac { 10 } { \sqrt { 101 } }$ 
E)  $- \frac { 10 } { \sqrt { 101 } }$ B

Question 4

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 5

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 6

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 7

Rewrite the angle $\frac { 2 \pi } { 3 }$ radians in degree measure.

Accepted Answer

A)  $240 ^ { \circ }$ 
B)  $80 ^ { \circ }$ 
C)  $120 ^ { \circ }$ 
D)  $60 ^ { \circ }$ 
E)  $300 ^ { \circ }$ 
A)  $240 ^ { \circ }$ 
B)  $80 ^ { \circ }$ 
C)  $120 ^ { \circ }$ 
D)  $60 ^ { \circ }$ 
E)  $300 ^ { \circ }$

Question 8

Determine the exact value of arctan (-1) .

Accepted Answer

A)  $\frac { \pi } { 4 }$ 
B)  $- \frac { \pi } { 2 }$ 
C)  $- \frac { \pi } { 4 }$ 
D)  0 
E)  $\frac { \pi } { 2 }$ 
A)  $\frac { \pi } { 4 }$ 
B)  $- \frac { \pi } { 2 }$ 
C)  $- \frac { \pi } { 4 }$ 
D)  0 
E)  $\frac { \pi } { 2 }$

Question 9

Determine the graph of $y = \frac { 1 } { 5 } \cos ( x )$.

Accepted Answer

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

Question 10

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 11

Convert the given angle measure from radians to degrees. Round to three decimal places. $\frac { 3 \pi } { 7 }$

Accepted Answer

A)  0.023° 
B)  77.143° 
C)  154.286° 
D)  38.571° 
E)  420.000° 
A)  0.023° 
B)  77.143° 
C)  154.286° 
D)  38.571° 
E)  420.000°

Question 12

A certain satellite orbits 13,000 miles above Earth's surface (see figure). Find the angle of depression $\alpha$ from the satellite to the horizon. Assume the radius of the Earth is 4000 miles. Round your answer to the nearest hundredth of a degree.

Accepted Answer

A)  $13.61 ^ { \circ }$ 
B)  $17.92 ^ { \circ }$ 
C)  $72.08 ^ { \circ }$ 
D)  $76.39 ^ { \circ }$ 
E)  $13.24 ^ { \circ }$ 
A)  $13.61 ^ { \circ }$ 
B)  $17.92 ^ { \circ }$ 
C)  $72.08 ^ { \circ }$ 
D)  $76.39 ^ { \circ }$ 
E)  $13.24 ^ { \circ }$

Question 13

Determine the quadrant in which the angle -191° 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 14

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)  $\sin \theta = - \frac { 5 } { 3 }$ 
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)  $\sin \theta = - \frac { 5 } { 3 }$

Question 15

Find the point $( x , y )$ on the unit circle corresponding to the real number $t = \frac { 11 \pi } { 6 }$.

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 16

Determine the graph of $y = \frac { 1 } { 3 } \cos ( x )$.

Accepted Answer

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

Question 17

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 18

Use the figure and a straightedge to approximate the value of cos1.75 .

Accepted Answer

A)  1.00 
B)  0.98 
C)  -0.18 
D)  -5.52 
E)  -5.61 
A)  1.00 
B)  0.98 
C)  -0.18 
D)  -5.52 
E)  -5.61

Question 19

If the sides of a rectangular solid are as shown, and $s = 6$, determine the angle, $\theta$, between the diagonal of the base of the solid and the diagonal of the solid. Round answer to two decimal places.

Accepted Answer

A)  $17.21 ^ { \circ }$ 
B)  $19.86 ^ { \circ }$ 
C)  $21.91 ^ { \circ }$ 
D)  $24.09 ^ { \circ }$ 
E)  $26.28 ^ { \circ }$ 
A)  $17.21 ^ { \circ }$ 
B)  $19.86 ^ { \circ }$ 
C)  $21.91 ^ { \circ }$ 
D)  $24.09 ^ { \circ }$ 
E)  $26.28 ^ { \circ }$

Question 20

Determine the quadrant in which the angle 3, given in radians, lies.

Accepted Answer

A)  1 
B)  3 
C)  4 
D)  2 
A)  1 
B)  3 
C)  4 
D)  2

Determine the graph of $y = \cos \left( \frac { 5 x } { 3 } \right)$ .

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

The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the line. Line Quadrant Evaluate: y=10x I \theta

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

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

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

Rewrite the angle $\frac { 2 \pi } { 3 }$ radians in degree measure.

Determine the exact value of arctan (-1) .

Determine the graph of $y = \frac { 1 } { 5 } \cos ( x )$ .

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

Convert the given angle measure from radians to degrees. Round to three decimal places. $\frac { 3 \pi } { 7 }$

Determine the quadrant in which the angle -191° lies.

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

Find the point $( x , y )$ on the unit circle corresponding to the real number $t = \frac { 11 \pi } { 6 }$ .

Determine the graph of $y = \frac { 1 } { 3 } \cos ( x )$ .

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

Use the figure and a straightedge to approximate the value of cos1.75 .

Determine the quadrant in which the angle 3, given in radians, lies.

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

Review of Graphs, Equations, and Inequalities

Filters

Exam 4: Trigonometric Functions

Determine the graph of y=cos⁡(5x3)y = \cos \left( \frac { 5 x } { 3 } \right)y=cos(35x​) .

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​

The terminal side of θ\thetaθ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of θ\thetaθ by finding a point on the line. Line Quadrant Evaluate: y=10x I \theta

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

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

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

Rewrite the angle 2π3\frac { 2 \pi } { 3 }32π​ radians in degree measure.

Determine the exact value of arctan (-1) .

Determine the graph of y=15cos⁡(x)y = \frac { 1 } { 5 } \cos ( x )y=51​cos(x) .

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

Convert the given angle measure from radians to degrees. Round to three decimal places. 3π7\frac { 3 \pi } { 7 }73π​

A certain satellite orbits 13,000 miles above Earth's surface (see figure). Find the angle of depression α\alphaα from the satellite to the horizon. Assume the radius of the Earth is 4000 miles. Round your answer to the nearest hundredth of a degree.

Determine the quadrant in which the angle -191° lies.

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 .

Find the point (x,y)( x , y )(x,y) on the unit circle corresponding to the real number t=11π6t = \frac { 11 \pi } { 6 }t=611π​ .

Determine the graph of y=13cos⁡(x)y = \frac { 1 } { 3 } \cos ( x )y=31​cos(x) .

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

Use the figure and a straightedge to approximate the value of cos1.75 .

If the sides of a rectangular solid are as shown, and s=6s = 6s=6 , determine the angle, θ\thetaθ , between the diagonal of the base of the solid and the diagonal of the solid. Round answer to two decimal places.

Determine the quadrant in which the angle 3, given in radians, lies.

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

Review of Graphs, Equations, and Inequalities

Filters

Determine the graph of $y = \cos \left( \frac { 5 x } { 3 } \right)$ .

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

The terminal side of $\theta$ lies on the given line in the specified quadrant. Find the value of the given trigonometric function of $\theta$ by finding a point on the line. Line Quadrant Evaluate: y=10x I \theta

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

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

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

Rewrite the angle $\frac { 2 \pi } { 3 }$ radians in degree measure.

Determine the graph of $y = \frac { 1 } { 5 } \cos ( x )$ .

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

Convert the given angle measure from radians to degrees. Round to three decimal places. $\frac { 3 \pi } { 7 }$

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

Find the point $( x , y )$ on the unit circle corresponding to the real number $t = \frac { 11 \pi } { 6 }$ .

Determine the graph of $y = \frac { 1 } { 3 } \cos ( x )$ .

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