Download Sample Questions, Exam #1, Math 1149 Find the arc length for the

Sample Questions, Exam #1, Math 1149
1. Find the arc length for the arc of a circle with a radius of 2 inches subtended by an angle of 30
degrees. (5 points)
2. Find the area of the sector of circle with the conditions in problem #6. (5 points)
3. Given that tan   4 , find the exact values for the following expressions: (3 points each)
2
a. sec 
b.


cot    
2

c.
cot 
1
Sample Questions, Exam #1, Math 1149
d.
csc 2 
4. Find the exact value for each of the following expressions. (10 points)

4
a.
sec 2
b.
tan
c.
1  cos2 30  csc2 225
6
5
7
 cot
4
4
5. List 5 angles that are coterminal with the angle 3π/4. (You may not use degree-equivalents of
angles given already in radians. These will be considered duplicates.) Draw the angle on the
graph below. (5 points)
2
Sample Questions, Exam #1, Math 1149
6. Find the exact value of each of the six trigonometric functions for an angle whose terminal side
passes through the point (5,-12). (5 points)
7. What is the domain and range of the six trigonometric functions? List both for each function.
(10 points)
3
Sample Questions, Exam #1, Math 1149
8.
For any trigonometric function, what does f ( a  2 ) equal? (2 points)
9. a. Find the length of arc of the circle subtended by an angle of 14°17’43” if the radius of the
circle is 25 meters.
b. Find the area of the sector of a circle subtended by an angle of 5 radians for a circle of 17
inches radius. What is the original angle in degrees-minutes-seconds?
10. Given that cot  
a.


tan    
2

b.
csc
1
, find the exact values of the following:
2
4
Sample Questions, Exam #1, Math 1149
c.
1  sin 2   cos2 


 
2

d. sec  sin 
11. Find the exact value of the following expressions (no decimals!)
a.
sec

3
 2 csc

4
2
2
b. 1  cos 30  cos 60
c.
sin     cos 5 
d.
 17
cos  
 4

 3 
  sin   

 2 
12. Given the point (2,-2) on the terminal side of an angle, find the exact values of all six
trigonometric functions.
5
Sample Questions, Exam #1, Math 1149
13. For an angle for which sec  
6
4
, and sin   0 , find the remaining trigonometric functions.
3
14. For f ( x )  cos x ,
a. Is f odd, even or neither?
b. Is its graph symmetric? To what axis?
c. What is the range of f?
d. If f ( a ) 
1
, find the exact value of f ( a ) .
4
e. If f ( ) 
1
, find f ( )  2 f   2  
2


f   
2

Sample Questions, Exam #1, Math 1149
7
15. The tallest tower built before the era of television mast, the Eiffel Tower was completed on
March 31, 1889. Find the height of the Eiffel Tower (before a television mast was added to the
top) using the fact that 80 feet away from the center of the tower, and angle of elevation of
85.361° was needed to look at the top.
16. A length of arc cut from a circle of radius 30 feet is 60 feet long. Find the angle that the arc
makes on the original circle. Give the angle in radians. (4 points)
17. A chocolate cream pie with a radius of nine inches has a slice cut out of it. The angle of the slice
cut out is 12°. Find the area of the slice of pie removed. (6 points)
Sample Questions, Exam #1, Math 1149
8
18. Given the csc  3 , find the five remaining trig functions. Assume that the angle is acute. (7
points)
19. For the trigonometric functions indicated, give the sign of each function in each quadrant on the
graph below the function. (12 points)
sin 
tan 
20. Find the values of the five remaining trigonometric functions for sec  
points)
sec
4
, and tan   0 .
3
(7
Sample Questions, Exam #1, Math 1149
9
21. a) If you are 350 feet from an office building at the base of a hotel, and the angle of elevation to
the top of the building is 48°, how tall is the office building? b) If you are now standing on the
roof of the hotel and the angle of elevation to the top of the office building is 23°, how tall is the
hotel? Round your answers to the nearest foot. (10 points)
 2 
 in the calculator. Round to 3 decimal places. (2 points)
 15 
22. a. Find sec 
b. Simplify without a calculator: cot 40 
sin 50
(Show all work for full credit.) (4 points)
sin 40
2
2
c. Simplify without a calculator: 1  sec 36  tan 36 (4 points)
 
 3 
  tan   (4 points)
2
 4 
d. Give exact value without a calculator: sin 
Sample Questions, Exam #1, Math 1149
23. a. Graph 480° in standard position. (5 points)
b. What is the reference angle? (2 points)
c. List two coterminal angles. (2 points)
d. Find tan 480 (2 points)
24. a. What is the range of the sine function? (1 point)
b. What is the domain of the cotangent function? (1 point)
c. What is the period of the secant function? (1 point)
d. Is the tangent function odd or even? (1 point)
 7 
2  17 
  cos  
 (2 points)
 4 
 3 
e. Simplify. tan  
10
Sample Questions, Exam #1, Math 1149
11
25. Martin and Maddie decide to build a circular garden in their backyard. The circular area has a
radius of 20 feet. In order to see into the garden, they have lowered the wall surrounding the
garden to just a small lip for an arc of 98°22’45”. That same sector of the garden will be left
unplanted so that they can install a bench and a bird bath.
a) Find how long the wall will be around the rest of the garden.
b) Find the square area of the garden that is being left unplanted.
26. Given an acute angle with sin  
1
, find the remaining six trig functions.
3
Sample Questions, Exam #1, Math 1149
27. The angle of elevation of the Sun is 35.1° at the instant it casts a shadow 789 feet long of the
Washington Monument. Use this information to calculate the height of the monument. Then
determine how long the shadow would be for a building only 100 feet high.
28. If tan  4 and sin   0 , what quadrant is θ in? Find the values of the remaining trig
functions.
12
Sample Questions, Exam #1, Math 1149
13
29. For the angle θ = -225°, find the following:
a) Two co-terminal angles
b) An appropriate reference angle
c) The exact value of tan θ.
d) The exact value of a point on the terminal side the ray forming the angle.
e) The exact value of sec 2   tan 2 
30. Find the exact value of the expression. State the rules used for each simplification.
 9
tan( 6 )  cos 
 2
   17
  cos  
   4

 3
  sin  

 2



Sample Questions, Exam #1, Math 1149
31. a) What is the range of the tangent function?
b) What is domain of the sine function?
c) Is the secant function odd or even?
d) What is the periodicity of the cotangent function?
e) For what values is cosecant not defined?
14