Name___________________________________
Algebra 2/Trig
Date___________
Practice with Sum, Diff, Dbl ID’s
5
, what is cos2A ?
3
1
1
(3)
(4)
3
3
1. If A is a positive acute angle and sin A 
(1)
1
9
1
9
(2)
2. The expression cos 40 cos10  sin 40 sin10 is equivalent to
(1) cos30
(2) cos50
(3) sin30
3. If x is an acute angle and sin x 
(1)
25
169
(2)
119
169

4. The expression cos 180  x
(1) sin x
(2)  sin x
(4) sin50
12
, then cos2x equals
13
(3)
25
169
(4)
119
169
 is equivalent to
(3) cos x
(4)  cos x
4
5
, tan B 
, and angles A and B are in Quadrant I, what is the value of
5
12
sin A  B  ?
5. If sin A 
(1)
63
65
(2)
63
65
(3)
33
65
(4)
6. For all values of A for which the expressions are defined,
equivalent to
(1) 1
(2) sin A
(3) cos A
33
65
sin2A
 sin A is
cos A
(4) 2sin A
Find the exact value of each of the following.

4
, where  is in Quadrant I, evaluate cos   60
5
.
7.
Given sin  =
8.
2
Given cos  =  , where  is in Quadrant II, evaluate sin   30 .
3
9.
Given that cos  = 

evaluate cos (  +  ).

2
4
and sin  = , where both  and  are in Quadrant II,
3
5
3
3
and cos  =  , where 180    270 and 90    180 ,
4
5
evaluate sin (  -  ).
10.
If sin  = 
11.
cos200 cos50  sin200 sin50
12.
sin190 cos35  cos190 sin35
13. cos165
14. sin285
15. Find all values of x in the interval 0  x  360 that satisfy the equation
3cos x  sin2x  0 .
16. Find all values of  in the interval 0    360 that satisfy the equation
3cos2  2sin  1  0 , and round all answers to the nearest hundredth of a degree.
[Only an algebraic solution can receive full credit.]
17. Find all values of x in the interval 0  x  360 that satisfy the equation
3cos2x  cos x  2 . Express your answers to the nearest degree.
ANSWERS
1) (2)
10)
94 7
20
11)
 3
2
12)
 2
2
13)
 2 6
4
2) (1)
3) (4)
4) (4)
5) (1)
6) (2)
7)
3 4 3
10
14)
 2 6
4
8)
15  2
6
15)
90 , 270 
9)
4 5 6
15
16)
90 , 221.81 , 318.19 
17)
0 , 146 , 214 