Name: ___________________________________
Date: _____________________
PreCalc
REVIEW: SUM/DIFFERENCE FORMULAS
#1-6. Using the sum & difference formulas, condense each of the following and express as a trig
function of a single angle.
1.
sin 97o cos43o  cos97o sin 43o
2.
cos72o cos130o  sin 72o sin130o
3.
tan140o  tan 60
1  tan140o tan 60
4.
sin
5.
cos

6
cos

7
 sin

6
sin

5
tan

6.
7
cos

3
1  tan
2

2
 cos sin
3
5
3
 tan

3

tan
4

4
#7-8. Use the sum & difference formulas with unit circle values to find exact answers for the
following:
o
o
7. tan(105 )
8. sin 345
#9-11. Given: csc  
9.
sin(   )
#12-13. If sin   
12.

13 
3 3
,
    , and tan    ,
   2 , find the following:
5
2
4
2
10.
cos(    )
11.
tan(   )
3
and  is in the third quadrant, find the following:
5
cos(  )
3
13.
tan 2
#14-18. Verify the following identities.
3
 x)   cos x
2
14.
sin(  x)  sin x
15.
sin(
16.
cos(300  x)  cos(30o  x)  3 cos x
17.
sin(    )
 cot   cot 
sin  sin 
18.
cos(   )  cos(   )  2cos  cos 
Name: ___________________________________
Date: _____________________
PreCalc
#19-21. Solve each of the following equations over the interval 0, 2  .
19.

 1


sin  x    sin  x   
6
6 2


20.
tan  x     2sin  x     0
21.

3


sin  x    cos  x 
2
2



0

REVIEW: DOUBLE ANGLE FORMULAS
#1-4. Using the double angle identities, condense each of the following and express as a trig
function of a single angle.
1.
2sin 97o cos 43o
2.
 cos 72   sin 72 
3.
2 tan140o
1  tan 2 140o 
4.
2 

2  cos
 1
3 

o 2
o 2
2
#5-7. Use the double angle identities with unit circle values to find exact answers for the
following:
5.
tan(420o )
6.
#8-9. Given: csc  
9.
10.
cos(2 )
7.
cos  480o 
13 
3 3
,
    , and tan    ,
   2 , find the following:
5
2
4
2
sin(   )
#10-11. If sin   
10.
sin 660o
cos(    )
3
and  is in the third quadrant, find the following:
5
11. tan 2
#12-15. Verify the following identities.
12.
 sin x  cos x 
2
 1  sin 2 x
14. sin 2 x   tan x 1  cos 2 x 
1  tan 2 x
 cos 2 x
13.
1  tan 2 x
1  tan 2 x
15. cot 2 x 
2 tan x
11.
tan(   )
Name: ___________________________________
Date: _____________________
PreCalc
Answers: 1.
sin190o
 13
cos 
 42
33
10. 
65



5.
20.
0,  ,
6.
11.
 5
3
,
3
2.
tan
16
63
7
12
7.
12.
21.
cos10o
4
,
2 3
4  3 3
10
 5
4
3.
tan 80o
2 6
4
8.
13.
 7 
 sin 

 15 
4.
24
7
19.

9.
 5
3
,
3
16
65