Question 1

​Sketch the graph of the function below, being sure to include at least two full periods. ​
​y = 2 cos​( x -   )
​   ​

Accepted Answer

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

Question 2

Use a graphing utility to select the graph of the two equations in the same viewing window.Use the graphs to determine whether the expressions are equivalent. ​   ​

Accepted Answer

A) ​   The expressions are equivalent except
Sinx = 0, y1 is undefined. 
B) ​   The expressions are equivalent except when sinx = 0, y1 is undefined. 
C) ​   The expressions are equivalent except when
Sinx = 0, y1 is undefined. 
D) ​   The expressions are equivalent except when sinx = 0, y1 is undefined. 
E) ​   The expressions are equivalent except when sinx = 0, y1 is undefined. 
A) ​   The expressions are equivalent except
Sinx = 0, y1 is undefined. 
B) ​   The expressions are equivalent except when sinx = 0, y1 is undefined. 
C) ​   The expressions are equivalent except when
Sinx = 0, y1 is undefined. 
D) ​   The expressions are equivalent except when sinx = 0, y1 is undefined. 
E) ​   The expressions are equivalent except when sinx = 0, y1 is undefined.

Question 3

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound. ​

Accepted Answer

A) ​   As x → ∞, f(x) → 0. 
B) ​   As x → ∞, f(x) → 0. 
C)    As x → ∞, f(x) → 0. 
D) ​   The function f(x) is unbounded as x → ∞. 
E) ​   The function f(x) is unbounded as x → ∞. 
A) ​   As x → ∞, f(x) → 0. 
B) ​   As x → ∞, f(x) → 0. 
C)    As x → ∞, f(x) → 0. 
D) ​   The function f(x) is unbounded as x → ∞. 
E) ​   The function f(x) is unbounded as x → ∞.

Question 4

Use an inverse trigonometric function to write θ as a function of x. ​   ​
A = x + 5
B = 10
​

Accepted Answer

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

Question 5

State the quadrant in which θ lies if   > 0 and   > 0.

Accepted Answer

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

Question 6

Find the values of θ in degrees   and radians   without the aid of a calculator. sec θ =   and cot θ = 1
​
​

Accepted Answer

A) 45° =   
B) ​90° =   
C) ​0° = 0 
D) ​60° =   
E) ​30° =   
A) 45° =   
B) ​90° =   
C) ​0° = 0 
D) ​60° =   
E) ​30° =

Question 7

Evaluate each function.Round your answers to four decimal places. ​
Tan15.7° and cot74.3°
​

Accepted Answer

A) 0.4811 and 0.4811 
B) 0.3311 and 0.3311 
C) 0.2811 and 0.2811 
D) 0.3811 and 0.3811 
E) 0.4311 and 0.4311 
A) 0.4811 and 0.4811 
B) 0.3311 and 0.3311 
C) 0.2811 and 0.2811 
D) 0.3811 and 0.3811 
E) 0.4311 and 0.4311

Question 8

The displacement from equilibrium of an oscillating weight suspended by a spring and subject to the damping effect of friction is given by ​   where y is the displacement in centimeters and t is the time in seconds (see figure).Find the displacement when   .(Round your answer two decimal places.)
​
​   ​
​

Accepted Answer

A) 0.71 cm 
B) 1.11 cm 
C) 1.31 cm 
D) -0.91 cm 
E) 0.91 cm 
A) 0.71 cm 
B) 1.11 cm 
C) 1.31 cm 
D) -0.91 cm 
E) 0.91 cm

Question 9

Select the graph of the function.(Include two full periods.) ​   ​

Accepted Answer

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

Question 10

Use a graphing utility to graph the function below.

Accepted Answer

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

Question 11

Evaluate (if possible) the sine, cosec, and tangent of the real number. ​   ​

Accepted Answer

A)    corresponds to the point   .   
B)    corresponds to the point   .   
C)    corresponds to the point   .   
D)    corresponds to the point   .   
E) Not possible 
A)    corresponds to the point   .   
B)    corresponds to the point   .   
C)    corresponds to the point   .   
D)    corresponds to the point   .   
E) Not possible

Question 12

Find the reference angle   , and sketch   and   in standard position. ​   ​

Accepted Answer

A)      
B)      
C)    = 35     
D)    = 65     
E)    = 55     
A)      
B)      
C)    = 35     
D)    = 65     
E)    = 55

Question 13

The graph of y = 3cscx can be obtained on a calculator by graphing the reciprocal of y = 3sinx.
​

Accepted Answer

A) True 
 B)False

Question 14

Find a model for simple harmonic motion satisfying the specified conditions. ​
Displacement (t = 0): 0
Amplitude: 5 meters
Period: 10 seconds
​

Accepted Answer

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

Question 15

Select the graph of the given function.Make sure to include at least two periods.   ​

Accepted Answer

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

Question 16

Evaluate the trigonometric function.Round your answer to four decimal places. ​
Cot 171°
​

Accepted Answer

A) -5.3138 
B) -4.3138 
C) -6.3138 
D) -3.3138 
E) -5.8138 
A) -5.3138 
B) -4.3138 
C) -6.3138 
D) -3.3138 
E) -5.8138

Question 17

The displacement from equilibrium of an oscillating weight suspended by a spring is given by   , where y is the displacement in centimeters and t is the time in seconds.Find the displacement when   , rounding answer to four decimal places.

Accepted Answer

A) -3.7018 cm 
B) -6.4350 cm 
C) 23.8825 cm 
D) 2.9298 cm 
E) -1.6362 cm 
A) -3.7018 cm 
B) -6.4350 cm 
C) 23.8825 cm 
D) 2.9298 cm 
E) -1.6362 cm

Question 18

After leaving the runway, a plane's angle of ascent is 17o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places. ​

Accepted Answer

A) 1.72 minutes 
B) 1.19 minutes 
C) 2.24 minutes 
D) 0.65 minutes 
E) 0.68 minutes 
A) 1.72 minutes 
B) 1.19 minutes 
C) 2.24 minutes 
D) 0.65 minutes 
E) 0.68 minutes

Question 19

Evaluate the trigonometric function.Round your answer to four decimal places. ​   ​

Accepted Answer

A) 1.8637 
B) 3.8637 
C) 4.3637 
D) 6.8637 
E) 4.8637 
A) 1.8637 
B) 3.8637 
C) 4.3637 
D) 6.8637 
E) 4.8637

Question 20

Write an algebraic expression that is equivalent to   .

Accepted Answer

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

Sketch the graph of the function below, being sure to include at least two full periods. y = 2 cos( x - )

Use a graphing utility to select the graph of the two equations in the same viewing window.Use the graphs to determine whether the expressions are equivalent.

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound.

Use an inverse trigonometric function to write θ as a function of x. A = x + 5 B = 10

State the quadrant in which θ lies if > 0 and > 0.

Find the values of θ in degrees and radians without the aid of a calculator. sec θ = and cot θ = 1

Evaluate each function.Round your answers to four decimal places. Tan15.7° and cot74.3°

The displacement from equilibrium of an oscillating weight suspended by a spring and subject to the damping effect of friction is given by where y is the displacement in centimeters and t is the time in seconds (see figure).Find the displacement when .(Round your answer two decimal places.)

Select the graph of the function.(Include two full periods.)

Use a graphing utility to graph the function below.

Evaluate (if possible) the sine, cosec, and tangent of the real number.

Find the reference angle , and sketch and in standard position.

The graph of y = 3cscx can be obtained on a calculator by graphing the reciprocal of y = 3sinx.

Find a model for simple harmonic motion satisfying the specified conditions. Displacement (t = 0): 0 Amplitude: 5 meters Period: 10 seconds

Select the graph of the given function.Make sure to include at least two periods.

Evaluate the trigonometric function.Round your answer to four decimal places. Cot 171°

The displacement from equilibrium of an oscillating weight suspended by a spring is given by , where y is the displacement in centimeters and t is the time in seconds.Find the displacement when , rounding answer to four decimal places.

After leaving the runway, a plane's angle of ascent is 17^o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places.

Evaluate the trigonometric function.Round your answer to four decimal places.

Write an algebraic expression that is equivalent to .

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 1: Trigonometry

​Sketch the graph of the function below, being sure to include at least two full periods. ​ ​y = 2 cos​( x - ) ​ ​

Use a graphing utility to select the graph of the two equations in the same viewing window.Use the graphs to determine whether the expressions are equivalent. ​ ​

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound. ​

Use an inverse trigonometric function to write θ as a function of x. ​ ​ A = x + 5 B = 10 ​

State the quadrant in which θ lies if > 0 and > 0.

Find the values of θ in degrees and radians without the aid of a calculator. sec θ = and cot θ = 1 ​ ​

Evaluate each function.Round your answers to four decimal places. ​ Tan15.7° and cot74.3° ​

Select the graph of the function.(Include two full periods.) ​ ​

Use a graphing utility to graph the function below.

Evaluate (if possible) the sine, cosec, and tangent of the real number. ​ ​

Find the reference angle , and sketch and in standard position. ​ ​

The graph of y = 3cscx can be obtained on a calculator by graphing the reciprocal of y = 3sinx. ​

Find a model for simple harmonic motion satisfying the specified conditions. ​ Displacement (t = 0): 0 Amplitude: 5 meters Period: 10 seconds ​

Select the graph of the given function.Make sure to include at least two periods. ​

Evaluate the trigonometric function.Round your answer to four decimal places. ​ Cot 171° ​

The displacement from equilibrium of an oscillating weight suspended by a spring is given by , where y is the displacement in centimeters and t is the time in seconds.Find the displacement when , rounding answer to four decimal places.

After leaving the runway, a plane's angle of ascent is 17o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places. ​

Evaluate the trigonometric function.Round your answer to four decimal places. ​ ​

Write an algebraic expression that is equivalent to .

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Sketch the graph of the function below, being sure to include at least two full periods. y = 2 cos( x - )

Use a graphing utility to select the graph of the two equations in the same viewing window.Use the graphs to determine whether the expressions are equivalent.

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound.

Use an inverse trigonometric function to write θ as a function of x. A = x + 5 B = 10

Find the values of θ in degrees and radians without the aid of a calculator. sec θ = and cot θ = 1

Evaluate each function.Round your answers to four decimal places. Tan15.7° and cot74.3°

Select the graph of the function.(Include two full periods.)

Evaluate (if possible) the sine, cosec, and tangent of the real number.

Find the reference angle , and sketch and in standard position.

The graph of y = 3cscx can be obtained on a calculator by graphing the reciprocal of y = 3sinx.

Find a model for simple harmonic motion satisfying the specified conditions. Displacement (t = 0): 0 Amplitude: 5 meters Period: 10 seconds

Select the graph of the given function.Make sure to include at least two periods.

Evaluate the trigonometric function.Round your answer to four decimal places. Cot 171°

After leaving the runway, a plane's angle of ascent is 17^o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places.

Evaluate the trigonometric function.Round your answer to four decimal places.