PreCalculus
Midterm Review of Ch 6
1) Determine the exact value of each expression.


3 
a) sec  tan 1  
 

 3  
2) Establish each Identity.
1
1

 2 cot 2 x
a)
1  sec x 1  sec x
Name

 2 3  
b) sin  tan 1 
 

 3  
b)
3) Determine the exact value of cos     given cos   
csc x
 cos x
tan x  cot x
21
24 
3
,     and sin   
,  
.
25 2
2
5
 13
4) Use a Sum or Difference Formula to determine the exact value of tan 
 12

.

5
5) Use a Double-Angle Formula to determine the exact value of sin  2  given csc   , tan  0 .
2
1
 
6) Use a Half-Angle Formula to determine the exact value of cos   given sin    , tan  0 .
4
2
7) Express the sum sin  6   sin 10  as a product of sines and/or cosines.
 
8) Solve the equation 3csc    2 3  0 . Give a general formula(s) for all the solutions.
3


9) Solve the equation cot  2    1 on the interval 0    2 .
2

10) Solve the equation cos  2   5cos  3 on the interval 0    2 .
11) The seasonal variation in the length of daylight can be represented by a sine function. For example, the
daily number of hours (h) of daylight in a certain city in the U.S. can be given by
41 5  2 x 
h   sin 
,
4 3  365 
where x is the number of days after March 21 (disregarding leap year). On what 2 dates will there be about 10
hours of daylight?