Multiple Choice Practice
Trigonometric Functions
Algebra 2 Trigonometry Level
Algebra 2Trig Index | Regents Exam Prep Center


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Trigonometric Functions
 

Directions:  Choose the best answer.  Answer ALL questions (or only a few at a time), then use the BUTTON at the BOTTOM of the page to check your answers.  If you are told that an answer is incorrect, go back and redo that question and CHECK ANSWERS again.   You may CHECK ANSWERS at any time.
You may use a calculator when working on these problems.

1.   Expressed in radian measure, 235 is
       [1]                 [2]                  [3]                  [4] 
 

 

2.  What is the value of  sin(-240) ?

     [1]                     [2]                    [3]                    [4]   
 

 

3.  The value of     is

     [1]                       [2]                    [3]                    [4]  
 

 

4.  If the tangent of an angle is negative and its secant is positive, in which quadrant does the angle terminate?

     [1]  I                        [2]  II                    [3]  III                    [4]  IV  
 

 

5.  In the unit circle shown at the right, what are the coordinates of B?

     [1]             [3] 


     [2]  
          [4] 
    

 

 

 

6.  What is the value of    ?  

     [1]                      [2]                   [3]                [4] 

 

 

7.  What is the value of  

    [1]   1                            [2]                         [3]             [4] 
 

 

8.   Which expression is not equivalent to sin 150 ?

     [1]  sin 30                  [2]  - sin 210             [3]  cos 60         [4]  - cos 60
 

 

9.  A flower bed is planted in the shape of an arc along the edge of a circular walkway.  If the circle has a radius of 5 yards and the angle subtended by the arc measures 1.5 radians, what is the length, in yards, of the border?

     [1]  0.5                         [2]   2                   [3]  5                     [4]  7.5
 

 

10.  If  sin (x + 20) = cos x , the value of  x  is

     [1]  35                       [2]  45                 [3]  55                [4]  70
 

 

11.  The expression    is equivalent to

     [1]                    [2]             [3]                 [4] 
 

 

12.  The expression  (1 + cos x)(1 - cos x) is equivalent to

     [1]  1                          [2]              [3]               [4] 
 

 

 

13.  The expression  cos 80 cos 70  +  sin 80 sin 70   is equivalent to
  
     [1]
 cos 10                    [2]  cos 150             [3]  sin 10                [4]  sin 150 

 



 

14.   If       and   ,  then  sin (a - b)  equals
 
      [1]                         [2]                         [3]               [4] 
                                           

 

 

15.  The expression  sin2A - 2sinA  is equivalent to

     [1]  (sinA)(sinA - 2)     [2] (2sinA)(sinA - 1)    [3] (sinA)(2cosA - 1)    [4]  (2sinA)(cosA - 1)
 

 

16.  What value of x in the interval  0 < x < 180 satisfies the equation  ?

     [1]  -30                       [2]  30                      [3]  60                 [4]  150
 

 

17.  What is the amplitude of the graph of the equation  ?

     [1]  1/2                         [2]                         [3]  π                      [4]  2π
 

 

18.   A sound wave is modeled by the curve  y = 3sin4x.  What is the period of this curve?
     [1] 
 π                            [2]   π/2                     [3]  3                     [4] 
 

 

19.  The graph of the function   y = 3sin(2x +  π)   will display a horizontal shift of

     [1]  π  units to the right 
      [2] 
π  units to the left
     [3]   π/2 units to the right   
     [4] 
 π/2 units to the left
 

 

 

20.  A radio transmitter sends a radio wave from the top of a 50-foot tower.  The wave is represented by the graph shown at the right.  What is the equation of this radio wave? 
     [1]  
y = sin x       
      [2]  
y = 1.5 sin x
     
[3]  y = sin 1.5x
       [4]  y = 2sinx

           

   
 

 

21.  Which graph represents the function  f (x) = -sinx  in the interval  -π < x < π ?

      [1]                                                [3]          
     
                     
     

     [2]                                                 [4] 
                          

 

 

 

 

22.  Which value of x is not in the domain of the function defined by  y = tanx ?
     [1]  
π                         [2]   π / 2                       [3]  π / 3                     [4]  2π / 3  
 
23.  In ∆ABC, m<A = 120, b = 10", and c = 18".  What is the area of ∆ABC to the nearest square inch?
     [1]  
52                        [2]  78                           [3]  90                       [4]  156   
 
24.  In ∆ABC, m<A = 45, m<B = 30, and a = 10.  What is the length of side b?
     [1]                        [2]  
                      [3]                  [4]  
 
25.  You must cut a triangle out of a sheet of paper.  The only requirements you must follow are that one of the angles must be 60, the side opposite the 60 angle must be 40 centimeters, and one of the other sides must be 15 centimeters.  How many different triangle can you make?
     [1]  
1                           [2]  2                             [3]  3                       [4]  0   
 
26.   In ∆ABC,  sinA = 0.5, m<B = 45, and b = 20.  What is the length of side a?
     [1]                      [2]  
10                           [3]                 [4]    
 
27.  In triangle ABC, a = 2, b = 4 and c = .  Find the largest angle of the triangle.
     [1]  
60                         [2] 120                        [3]  150                   [4]  30
 
28.  Al is standing 50 yards from a maple tree and 30 yards from an oak tree in the park.  His position is shown in the diagram at the right.  If he is looking at the maple tree, he needs to turn his head 120 to look at the oak tree.  How many yards apart are the two trees?
     [1]  58.3        [2]  
65.2         [3]  70         [4]  75

 
29.  Find the exact value of  sec 60 + cot 45 + csc 30 .
     [1]  
1                           [2]  2                       [3]                        [4]  5
 
30.  Assuming an angle lies in Quadrant I, evaluate     as a fraction in lowest terms.
     [1]  
5/12                       [2]  5/13                  [3]  12/5                  [4]  13/5
 





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