Download MATH 1112

MATH 1112
FINAL EXAM REVIEW
I.
State the equation of the unit circle.
II.
If cot x  
III.
Simplify each expression.
IV.
V.
VI.
12
, find sin x for x in Quadrant II.
5
1.
 3 
sin   
 2 
2.
cos 
3.
sin150
4.
sin 660
5.
 3 
cos  

 4 
6.
cos0
7.
tan315
8.
cot 
9.
 5 
sec  

 6 
10.
csc0
Sketch the graph of each function on [0, 2 ) .
1.
y  sin x
2.
y  cos x
3.
y  tan x
4.
y  cot x
5.
y  sec x
6.
y  csc x
Simplify each expression.
1.
cos( )
2.
sin( )
3.
tan(  )
4.
sec(  )
2.

3
cos 1  

 2 
Evaluate each expression.
1.

2
arc sin  

 2 
3.
VII.
VIII.
IX.
X.

 3 
sec  cot 1    
 4 

4.
tan 1  1
Sketch at least one cycle of the graph of each function.
1.
y  3sin 2 x
2.
y  2cos  x     3
3.


y  tan  x  
3

4.
y  cot  2 x   
5.
y  2sec3x
Use the sum or difference identities to evaluate each expression.
1.
cos 75
3.
tan195
Let α be in Quadrant I, β in Quadrant III, cos  
1.
cos      ?
2.
sin      ?
3.
tan      ?
Change each sum or difference to a product.
1.
sin 68  sin32
2.
sin5x  sin3x
3.
cos12x  cos5x
4.
cos 20  cos 40
2.
sin 285
7
5
, and tan   .
25
12
XI.
XII.
XIII.
Let θ be in Quadrant II with sec   
1.
sin 2  ?
3.
tan 2  ?
13
.
5
2.
cos 2  ?
Evaluate each of the following expressions using the half-angle identities.
1.
sin112.5
3.
tan 67.5
2.
cos157.5
If the terminal side of θ passes through the point (-3,2), find sin 2 .
XIV. Solve each equation for 0  x  2 .
1.
cos 2x  1  sin x
2.
sin x cos x 
3.
2 cos 2 x  sin x  1  0
4.
3cot 2 2 x  1  0
1
2
XV. Solve ABC for the missing part.
1.
A  90, a  29, b  21, B  ?
2.
a  5, b  8, c  10, C  ?
3.
A  40, b  6, B  20, c  ?
XVI. Give the radian measure of an angle that subtends an arc of length 24 in a circle
of radius 8 .
XVII. Convert
5
to degrees.
12
XVIII. Convert 260 to radians.
XIX. Prove the following identities.
1.
sin  sec  tan 
2.
sec2  tan 2   sec2   sec 4 
3.
csc   sec 
 cot   tan 
sin   cos 
4.
 sin x  cos x 
2
 1  sin 2 x
XX. Simplify each expression.
1.
sec4 x  tan 4 x
sec2 x  tan 2 x
2.
cos  sin 

sin  cos 
3.
tan 
1  cos 2 
XXI. Change the product to a sum.
1.
6sin15 sin 45
2.
4sin3x cos 2x
 3 4
XXII. Let the point   ,  be a point on the terminal side of an angle θ in standard
 5 5
position. Find the sine and cosine of θ.
XXIII. If tan   0 and cos  0 , in what quadrant is θ?
XXIV. Give the reference angle for the indicated angle.
1.
211
3.
2.3
2.
5
9
2.
278
XXV. Find the quadrant in which the indicated angle lies.
1.
343
12
3.
5.43
4.

213
5
XXVI. Name one positive and one negative angle that is coterminal with the given angle.
1.
43
2.
13
12
ANSWERS:
I.
x2  y 2  1
II.
5
13
III.
1.
1
2.
-1
3.
1
2
4.

5.

6.
1
7.
-1
8.
Undefined
9.

10.
Undefined
IV.
1.
2.
2
2
2 3
3
3
2
3.
4.
5.
6.
V.
VI.
VII.
1.
cos
2.
 sin 
3.
 tan 
4.
sec
1.

2.
5
6
3.

4.

1.

4
5
3
2.

4
3.
4.
5.
VIII.
3.
IX.
X.
XI.
XII.
6 2
4
1.
1.
 3 3
 32
3 3
204

325
2.
 6 2
4
2.

323
325
323
36
3.

1.
2sin50 cos18
2.
2cos 4x sin x
3.
2 cos
17 x
7x
cos
2
2
4.
sin10
1.

2.

3.
120
119
2.

1.
120
169
2 2
2
119
169
2 2
2
2 2
2 2
3.
XIII.

12
13
XIV. 1.
2.
3.
4.
XV. 1.
3.
0,

6
, ,
5
6
 5
4
,
4
 7 11
2
,
6
,
6
  2 5 7 4 5 11
, ,
,
,
,
,
,
6 3 3 6 6 3 3 6
46.4
2.
97.9
2.
csc sec
15.2
XVI. 3
XVII. 75
XVIII.
13
9
XX. 1.
1
3.
csc sec
XXI. 1.
3 3 3
 
2
2
2.
2sin5x  2sin x
4
3
XXII. sin   , cos   
5
5
XXIII. IV
XXIV. 1.
3.
XXV. 1.
3.
2.
4
9
II
2.
I
IV
4.
III
31
.84
XXVI. *Answers may vary. I have given a couple of responses only.
1.
317, 403
2.
37 11
,
12
12