Integrated Math 3 Honors
Sullivan Unit 5 Review
Verify the identity.
1. 𝑐𝑠𝑐 2 𝑢 − cos 𝑢 sec 𝑢 = 𝑐𝑜𝑡 2 𝑢
2. (1 + 𝑡𝑎𝑛2 𝑢)(1 − 𝑠𝑖𝑛2 𝑢) = 1
3. tan 𝜗 ∙ csc 𝜗 = sec 𝜗
cos(𝛼+𝛽)
4.
= cot 𝛽 − tan 𝛼
cos 𝛼 sin 𝛽
5. (sin 𝑥 + cos 𝑥)2 = 1 + sin 2𝑥
sin 2𝑥
6.
= cot 𝑥
1−cos 2𝑥
Complete the identity.
(sec 𝑥+1)(sec 𝑥−1)
7.
=
2
𝑡𝑎𝑛 𝑥
csc 𝑥 cot 𝑥
8.
=
sec 𝑥
9. tan 𝑥(cot 𝑥 − cos 𝑥) =
sin 𝑥
cos 𝑥
10.
+
=
cos 𝑥
1+𝑡𝑎𝑛155° tan 35°
5𝜋
2 tan 8
1−𝑡𝑎𝑛2
Use a half-angle formula to find the exact value.
5𝜋
17. tan 165°
18. sin
12
Use a sum/difference formula to find the exact value.
19. sin 165°
20. tan 105°
Use the given information to find the exact value for ae.
a. sin(𝛼 + 𝛽)
d. sin 2𝛽
𝛼
b. tan(𝛼 − 𝛽)
e. 𝑐𝑜𝑠
2
c. cos(𝛼 + 𝛽)
21. sin 𝛼 =
cos 𝛽 = −
cos 𝛼 sin 𝛽
5. (sin 𝑥 + cos 𝑥)2 = 1 + sin 2𝑥
sin 2𝑥
6.
= cot 𝑥
1−cos 2𝑥
Complete the identity.
(sec 𝑥+1)(sec 𝑥−1)
7.
=
2
𝑡𝑎𝑛 𝑥
csc 𝑥 cot 𝑥
8.
=
sec 𝑥
9. tan 𝑥(cot 𝑥 − cos 𝑥) =
sin 𝑥
cos 𝑥
10.
+
=
Solve the equation on the interval [0, 2𝜋).
23.
24.
25.
26.
√2
cos 2𝑥 =
2
2𝑠𝑖𝑛2 𝑥 = sin 𝑥
2𝑐𝑜𝑠 2 𝑥 + sin 𝑥 − 2 = 0
𝑠𝑖𝑛2 𝑥 − 𝑐𝑜𝑠 2 𝑥 = 0
Name_________________________________
Period__________Date____________________
Use a half-angle formula to find the exact value.
5𝜋
17. tan 165°
18. sin
12
Use a sum/difference formula to find the exact value.
19. sin 165°
20. tan 105°
Use the given information to find the exact value for ae.
a. sin(𝛼 + 𝛽)
d. sin 2𝛽
𝛼
b. tan(𝛼 − 𝛽)
e. 𝑐𝑜𝑠
2
c. cos(𝛼 + 𝛽)
21. sin 𝛼 =
1+𝑡𝑎𝑛155° tan 35°
5𝜋
2 tan 8
5𝜋
8
7
25
40
cos 𝛽 = −
sin 𝑥
Use trigonometric identities and the unit circle to find
the exact value.
11. cos 20° cos 40° − sin 20° sin 40°
12. 2 sin 75° cos 75°
2𝜋
7𝜋
2𝜋
7𝜋
13. sin cos − cos sin
9
18
9
18
14. 𝑐𝑜𝑠 2 112.5° − 𝑠𝑖𝑛2 112.5°
tan 155°−tan 35°
15.
1−𝑡𝑎𝑛2
, 𝛽 lies in quadrant 3
41
5𝜋
8
Verify the identity.
1. 𝑐𝑠𝑐 2 𝑢 − cos 𝑢 sec 𝑢 = 𝑐𝑜𝑡 2 𝑢
2. (1 + 𝑡𝑎𝑛2 𝑢)(1 − 𝑠𝑖𝑛2 𝑢) = 1
3. tan 𝜗 ∙ csc 𝜗 = sec 𝜗
cos(𝛼+𝛽)
4.
= cot 𝛽 − tan 𝛼
16.
, 𝛼 lies in quadrant 2
Find all solutions of the equation.
22. 9 cos 𝑥 + 6√2 = 7 cos 𝑥 + 5√2
Integrated Math 3 Honors
Sullivan Unit 5 Review
cos 𝑥
7
25
40
sin 𝑥
Use trigonometric identities and the unit circle to find
the exact value.
11. cos 20° cos 40° − sin 20° sin 40°
12. 2 sin 75° cos 75°
2𝜋
7𝜋
2𝜋
7𝜋
13. sin cos − cos sin
9
18
9
18
14. 𝑐𝑜𝑠 2 112.5° − 𝑠𝑖𝑛2 112.5°
tan 155°−tan 35°
15.
16.
Name_________________________________
Period__________Date____________________
, 𝛼 lies in quadrant 2
41
, 𝛽 lies in quadrant 3
Find all solutions of the equation.
22. 9 cos 𝑥 + 6√2 = 7 cos 𝑥 + 5√2
Solve the equation on the interval [0, 2𝜋).
23.
24.
25.
26.
√2
cos 2𝑥 =
2
2𝑠𝑖𝑛2 𝑥 = sin 𝑥
2𝑐𝑜𝑠 2 𝑥 + sin 𝑥 − 2 = 0
𝑠𝑖𝑛2 𝑥 − 𝑐𝑜𝑠 2 𝑥 = 0