King Fahd University of Petroleum and Minerals
Prep-Year Math Program
Math 002 - Term 151
Recitation (7.1)
Question1:
 4 3
If the terminal side of an angle  intersects the unit circle at the point   ,   , then
 5 5
Find the exact value of sec( )  tan( ) .
Question2:
sin 44  cos134  sin (510) .
a)
Find the exact value of
b)
If csc x  3 , find all possible values of
Question3:
Write csct
in terms of tan t ,
where
 t 
sin x  cos x
sec x
3
.
2
Question4:
Determine whether the function is even, odd, or neither.
x  sin x
f ( x)  2 x tan x  3sec x
A) f ( x) 
B)
cos x
Question5:
King Fahd University of Petroleum and Minerals
Prep -Year Math Program
Math 002 - Term 151
Recitation (7.2)
Question1
Simplify the following expression
2
 sec  tan    1  ?
sec csc  tan  csc
Question2
Verify the following identities:
2
2
a)  sin   csc    cos  sec   tan 2   cot 2   7
b)
1  cos x

 csc x  cot x ,0  x 
1  cos x
2
Question3
sin 2 ( x)  cos 2 ( x)

sin( x)  cos( x)
a)
b)
c)
d)
e)
 sin   cos
2sin 
sin   cos 
cos   sin 
sin   cos 
Question4:
sec x  1 sec x  1


sec x  1 sec x  1
4csc x cot x
a)
b)
4sec x tan x
c)
4csc x cot x
d)
8sec x tan x
e)
2sec x tan x
King Fahd University of Petroleum and Minerals
Prep -Year Math Program
Math 002 - Term 151
Recitation (7.3)
Question1
Given sec  
13
3
, in quadrant II, and sin(  )  ,  in quadrant II, find sec     .
12
5
Question2
Find the value of: sin  210  x   cos 120  x  for any angle x.
Question3
 3

 3

    cos 
 
 2

 2

Simplify sin 
Question4
Find the exact value of the following expressions:
a ) cos(165)
b) sin13 sin 73  sin 77 sin17
c)
1  tan 69 tan 66
tan 69  tan 66
Question5
King Fahd University of Petroleum and Minerals
Prep -Year Math Program
Math 002 - Term 151
Recitation (7.4)
Question1
x
5
3
If csc x   , where
 x  2 , then find tan 2 x, cos .
2
4
2
Question2
3
cos 2  and  terminates in quadrant III, then find sin   cos
4
Question3
3 
 3
Find the exact value of:  sin  cos 
8
8 

2
Question4
2
Verify the following identity: sin
Question5
x
x
(1  sec x)2  cos2 tan 2 x
2
2
King Fahd University of Petroleum and Minerals
Prep -Year Math Program
Math 002 - Term 151
Reduction identity
a sin x  b cos x  k sin  x   
where k  a 2  b 2 and  is determined by: cos 
Or tan 
a
a 2  b2
and sin  
b
a 2  b2
b
where  can be detrmined from the quadrant that contains the point (a, b)
a
Question 1
x
3
Given the function f ( x)  2sin  2 3 cos
x
3
a) Rewrite f ( x) in the form f ( x)  k sin(bx   )
b) Find the amplitude, the phase shift, the period, and the range for the graph of f ( x) .
Question 2
If sin 20  3 cos 20  k sin  , 0    90 . Then k and  are equal to
a) 2, 40
b)
2, 20
c) 1  3, 20
d) 2, 20
e) 2, 30
King Fahd University of Petroleum and Minerals
Prep-Year Math Program
Math 002 - Term 151
Recitation (7.5)
Question1
Find the exact value of
Question2
Find the exact value of

 4
 12  
tan sin 1     cos 1    .
 5
 13  

3 

sec1  2   tan 1  tan

5 

Question3
Verify the identity
2 x 1  x2
tan ( 2cos x) 
.
2x2 1
1
Question4
Question5
 2 3 

1 
csc1 
  cos  sin  
5

 3 
A)
B)
C)

20
2

15


30
D)
E)
2
15
3
20
King Fahd University of Petroleum and Minerals
Prep-Year Math Program
Math 002 - Term 151
Recitation (7.6 & 7.7)
Question1
Solve the following equations
x
a) sin  cos x  1, for 0  x   .
2
b) sin 2 x  sin x  2cos x  1  0 , where 0  x  2
x
c) tan  1  cos x , where 0  x  2 .
2
Question2
Solve the equations:
arcsin 2 x  arccos x 

2
Question3
The sum of all solutions of the equation 2cos 2 x sin 3 x  2cos3 x sin 2 x  3 in the
interval [ ,  ] is:

4
2
A)
B)
C)


3
3
3
D)

E)
2
3
Question4
1
3
If cos 1 x  tan 1 3  sin 1 , then x 
A)
2 2 3
6
B)
2 2 1
6
D)
2 2 1
6
E)
2 2 3
6
C)
4  2
6