Download Chapter 4A Blank Review

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PreCalculus: Chapter 4 Practice Test (1)
1. Indicate whether each is True or False.
 4
_____ a) cot  
 3

 3

_____ b)
 sin  

2
_____ c) cos 1 1  0
_____ d) csc
_____ e) 2    3  cos   0
_____ f) cot  
 sec
5
12
csc 
sec 
 
 sin   
2
 2
______ h) For    
3
, tan   tan     .
2
2
2
 sec
1
7
7
______ j) cos  15  
1
sec15
______ g)  sin
______ i) tan
12
 sin 2 

______ k) If cos  0 and sin   0 , then
3
   2 .
2
2. Evaluate the other five trigonometric functions of  if sec  3.5 and csc  0 .
3. Let f    TRIG where TRIG can be replaced by any of the six trigonometric functions. Which
function(s) could replace TRIG in each situation?
 
 4 
 4 
a) f    1
b) f  
f 

4
 3 
 3 
c) f 1  2  

6
d) f    0 for

2
 
e) f    f   2 
f) The domain of f   is  ,   .
g) f   3   f  
3
 4 
h) 2 f 

 6  f  6 


 4 


i) f    co-f     , where co-f is the cofunction of f .
2

j) f   
1
, where co-f is the cofunction of f .
co-f  
4. Verify.
1  sin 
1  sin 
a)
1
 sec   tan 
sec   tan 
b)
 sec   tan  
c)
1  sin x
cos x

 2sec x
cos x
1  sin x
d)
1
 sec2 
sin   csc   sin  
e)
1
1

 2sec 2 
1  sin  1  sin 
f) csc 4   csc 2   cot 4   cot 2 
2

5. Let f  x   x3   2 x and g  x   sin x . Show that all the zeros of f are also zeros of g .
6. Identify all asymptotes and intercepts of the rational function f  x  
2 x 2  10 x  12
.
x3  10 x 2  24 x
7. Identify all asymptotes and intercepts on the interval 0, 2  of the trigonometric function
f  x   tan x .
8. From a point 150 ft in front of a building, the angles of elevation to the top of the building and to the
top of the flagpole atop the building are 42° and 47°, respectively. Draw a figure. Label the height
of the building and the flagpole with appropriate variables. Find the height of the flagpole to the
nearest tenth of a foot.
9. Explain why each of the following is not possible.
8
3
a) It is given that sin  
and tan   .
10
4
b) It is given that cos  
5
and tan   0 .
4
c) It is given that sin   
10. Given cos  
8
and the terminal side of  lies in Quadrant II.
19
8
, evaluate tan  using two methods.
17
a) Right triangle trigonometry
b) A Pythagorean identity
11. Find all values of  on the interval 0, 2  such that cos  0.2725 .
12. Find all values of x on the interval 0, 2  such that csc x  1.3784 .
13. A tunnel for a highway is to be cut through a mountain, which is 14,411 feet high. At a distance of 2
miles from the base of the mountain, the angle of elevation to the summit is 36. From a distance of
one and a half miles on the opposite side of the mountain, the angle of elevation is 47. Find the
length of the tunnel to the nearest foot.
36
2 mi
47
1.5 mi