Algebra II: Review Sheet
Trigonometric Functions
A) Find θ to the nearest second.
1.) tan θ = .7465
2.) cos θ = .5772
3.) sin θ = .3213
4.) tan θ = 1.2345
B) Find the value of x to 4 decimal places
1.) cos 504452
2.) sin 315221
3.) cos 53468
4.) tan 714633
C) Find x to the nearest tenth. (All angle measures in degrees/minutes/seconds)
x
1.)
2.)
3.)
4.)
15
40
x
18
35°
x°
24
42°
20
x°
D) Find sin θ, cos θ, tan θ, csc θ, sec θ, cot θ (Write the formulas)
1.)
2.)
Ө
61
13
5
5
12
Ө
12
6
F) Solve for x. SKIP THIS SECTION
1.) sin(x + 20) = cos(4x + 5)
2.) csc(2x – 8)=sec(4x + 38)
E) Name the quadrant in which  A lies.
1.) sin θ >0 and cot θ >0
2.) csc θ <0 and sec θ < 0
3.) cos θ <0 and sin θ >0
4.) tan θ <0 and sec θ <0
3.) tan 4x = cot 70
G) Write the following expressions as functions of acute angles whose measure is less than 45 .
1.) cos 78
2.) sec 125
3.) tan 256
4.) sin 280
H) Given the following points located on the unit circle, find sin θ, cos θ, tan θ, csc θ, sec θ, cot θ.
1.) ( 3 ,1)
2
2.)  ,
3
5

3 
I) Sketch the angle and determine the quadrant in which the terminal side lies.
1.) 140
2.) 97
3.) 315
4.) 168
5.)  475
184
6.)
J) The formula for finding the length of an arc is:  
s
r
or s = Өr
1.) In a circle, the length of a radius is 4cm. Find the length of an arc intercepted by a
central angle whose measure is 1.5 radians.
2.) In a circle, a central angle of 4.2 radians intercepts an arc whose length is 6.3 meters.
Find the length of a radius in meters.
3.) If Ө= 2.5 and r = 4, find s.
4.) If s = 12 and Ө=6, find r.
K) Change each angle from degrees to radians.
1.) 120
2.)  50
3.) 315
4.) 135
L) Change each angle from radians to degrees.
1.)
5
4
2.)
5
6
3.)
M) Complete the table below:
θ
30
45
Radians
5
3

3
4.)

6
180

2
5.) 240
5.)
11
6
270
2
sin θ
cos θ
tan θ
csc θ
sec θ
cot θ
N) Express each function as a function of a positive acute angle.
1. cos
4
3
  17 

 15 
2. sin 
3.csc
11
4
sec 208
O) Find the exact value of the function.
1. cos 315
2. sin 135
3. tan 120
6. csc
5
3
7. cot
3
4
8. csc 
4. cot 190
5. tan(-115)
4. cos 225
5. sin 240
9. cot 210
10. sec 120
6.
P) Find two angles, one with positive measure and one with negative measure that are coterminal
with the given angle.
1. 560
2.  75
3.
 5
8
Algebra II: Review Sheet
Answer Key
A)1.) 364429
2.) 544446
3.) 184430
4.) 505928
B)1.) .6327
2.) .5280
3.) .5910
4.) 3.0372
C) 1.) x = 26.8
2.) x = 12.6
3.) x = 412435
4.) x = 3000
5
13
12
cosӨ=
13
5
tanӨ=
12
6 61
61
5 61
cosӨ=
61
6
tan  =
5
13
5
13
secӨ=
12
12
cotӨ=
5
D) 1.)sinӨ=
cscӨ=
E) 1.) quadrant I
2.) quadrant IV
F) 1.) x = 13
2.) x = 10
3
3
H) 1.) sinӨ= 1, cosӨ= 3 , tanӨ=
2.)QII
3.)
L)1.) 225 2.) 150

3
3.) quadrant II
4.) quadrant II
3.) cot 14°
4.) cos10°
2.) sinӨ=
3.) s = 10
2
5
2.) 
3
18
N) 1. -cos
cscӨ=
5
5
2
, cosӨ= , tanӨ=
3
3
2
3.) QIII 4.) QIII 5.)Q III 6.) QII
J) 1.) s = 6 2.) r = 1.5
K) 1.)
61
6
61
sec  =
5
5
cot  =
6
2.) sinӨ=
3.) x = 5
2.) –csc 35°
G)1.) sin12°
I) 1.) Q II
Trigonometric Functions
4.) r = 2
7
4
4.)
3.) 300
 2 

 15 
2. sin 
3.csc
 3
4
5.)
4.)  30

4
4
3
5.) 330
4. cot 10
5. tan(65)
2
2
2
3
2.
3. - 3
4. 5. 2
2
2
2
2 3
6.
7. undefined
8. undefined
9. √3
3
6. -sec 28
O)1.
P) 1. 960°, -160°
2. 285°, -435°
3.
 21 11
,
8
8
10. -2