Download YEAR END REVIEW TRIG 2

MATH 30-1
TRIG 2
YEAR END REVIEW
NUMERIC RESPONSE SECTION:
x
 2sin 3 x in radian mode, the largest x2
intercept, correct to the nearest tenth is _________.
1.
Using your graphing calculator to graph y 
2.
Given that x is an acute angle, the value of x , correct to the nearest degree, such that
sin x cot x  0.4 is _______.
3.
The number of solutions to the equation cos 3  
1
has over the interval 0    2
2
is ______.
4.
Given that tan    3 is a fourth quadrant angle, determine the exact value of
sin 2   cos 2  .
5.
Each of the trigonometric ratios listed below results in a value of zero, or it will be
undefined.
 
tan  
2
 3 
cot 

 2 
sin  
csc  2 
Use the following code to indicate that the value of the ratio is zero, or that the ratio is
undefined.
1 = the ratio is zero
2 = the ratio is undefined
RATIO:
________
________
________
________
 
tan  
2
 3 
cot 

 2 
sin  
csc  2 
6.
Each trigonometric expression below can be simplified to a single numerical value.
1.
cot 2 x  csc2 x
2.
sec2 x  tan 2 x
3.
sin x 
4.
1
1
cos 2 x  sin 2 x
7
7
tan x
sec x
When the numerical values of the simplified expressions are arranged in ascending
order, the expression numbers are ____,____,____, and ____.
WRITTEN RESPONSE:
2 tan x
sin(2 x)
 n
, where x  

,n I .
2
2
2
1  tan x cos x  sin x
4 2
1.
Prove algebraically that
2.
What is the exact value of tan 75
3.
Find the general solution to the equation sin(2 )  cos   0 . Express the solution in
degrees.
MULIPLE CHOICE SECTION.
1.
2.
Which of the following is true when if x positive and y negative,
A.
tan  
x
, terminates in quadrant II
y
B.
tan  
y
,  terminates in quadrant II
x
C.
tan  
x
, terminates in quadrant IV
y
D.
tan  
y
,  terminates in quadrant IV
x
The solution to 2cos x  3  0 , for 0  x  2 is
A. x 
B. x 
C. x 
D. x 

3

3

6

6
,x 
2
3
,x 
5
3
,x 
5
6
x
11
6
3.
If sin  
4
, find two possible values of cos .
13
A. cos  
153
13
B. cos   
153
13
C. cos   
153
13
D. none of the above
4.
If the left side of an identity is sin x csc x , then the right side of the identity could be
A. 0
B. 1
C. tan x
D. sin 2 x
5.
Angles x and y terminate in the same quadrant. If cos x 
sin( x  y ) is
A.
56
65
B.
59
60
C. 
56
65
D. 
59
60
3
13
and csc y  , then
5
12
6.
When the identity tan  2 A  
2 tan A

is verified for A  , the left and right sides of
2
1  tan A
6
the identity are
A. 0
B. 3
7.
C.
3
D.
1
3
sin 3 x
For the identity
 tan x to be valid, which of the following restrictions
cos x  cos3 x
must be stated?
A. cos x  0
B. cos x  0,1
C. cos x  1,1
D. cos x  0, 1,1
8.
The exact value of cos
A. cos
B. cos
C. cos
D. cos

3

3

3

3
cos
cos
sin
sin

4

4

4

4

12
can be determined by using
 sin
 sin
 cos
 cos

3

3

4

4
sin
sin
sin
sin

4

4

3

3
9.
If cot   
3
and sin   0 , then the value of (sin   cos  )2 is:
4
A.
49
25
B.
6
25
C.
7
5
D. 
10.
7
5
If the point  4, 2  lies on the terminal arm of an angle  in standard position,
determine the exact value of csc .
A. - 5
B. 
11.
5
2
C.
5
2
D.
5
The value of cos75 cos15  sin 75 sin15 is
A. 1
B.
1
2
C.
D. 0
3
2
12.
In the interval 0  x  2 , the solutions of the equation sin 2 x  sin x are
A. 0,
B.
13.
,
,
2 2

2
 3
2
,
, ,
2
3
2
The complete set of solutions for 6sin 2  3  0 , 0    2 , is
A.
B.
C.
D.
14.
2
 3
C. 0,
D.

 5
3
,
3
 5
6
,
6
  5 5
, , ,
6 3 6 3
 5 13 17
,
,
,
12 12 12 12
If 5sin x  2  6 cos 2 x where 0  x  2 , then one of the factors used to solve for x is
A. 3sin x  4
B. 2sin x 1
C. 6sin x 1
D. sin x 1
15.
Simplify
sin(   )


cos    
2


A. 1
B. 1
C. tan 
D.  tan 
16.
The expression sin x  cos 2 x csc x is equivalent to
A. sin 2 x
B. tan 2 x
C. csc x
D. sec x