Download Questions for Sections 7.1 and 7.2

Dammam Community College
MATH 012
Past Exam Questions
Sections 7.1& 7.2
3
, write cot  in terms of cos .
2
 cos 
Answer: cot =
1  cos 2 
1. For    
2. For   t 
3
, write csct in terms of tan t .
2
 1  tan 2 t
Answer: csc t =
tan t
sin x
1  cos x

in terms of csc x only.
1  cos x
sin x
Answers:  2 csc x
3. Write the expression
4. Write the expression
csc t  cot t 1  sin t

as a single trigonometric function.
sec t  tan t 1  cos t
Answer:  cot t
5. Write the expression
cos   sin  tan 
in terms of sec only.
cos 
Answer:  sec2 
6. If the terminal side of an angle  in standard position contains the point P  3,5 , find the value of
cot     sec    .
Answer: 
9  5 34
15
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Dammam Community College
MATH 012
7. The expression
a)
b)
c)
d)
e)
sec  tan  2
 csc  cot  2
sec  sin  2
 cos  tan  2
sec  csc 2
8. The expression
a)
b)
c)
d)
e)
1  sin 
is identical to
1  sin 
sin x
 cot x is identical to
1  cos x
csc x
 cos x
sin x
csc x  cot x
tan x
3

9. If x  sin  , where 0    , then the expression
2
2
12 x 2
9  4x 
2
3
simplifies to
2
a) tan 2  sec
b) tan 2  sin 
c) tan 2  cos
d) cot 2  sec
e) cot 2  sin 
sin 3 x  cos3 x
simplifies to
sin x  cos x
1  sin x cos x
1  2sin x cos x
1  2sin x cos x
1  sin x cos x
1  sin x cos x
10. The expression
a)
b)
c)
d)
e)
©12th April, 2010. DCC-KFUPM
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Dammam Community College
MATH 012
11. The expression
a)
b)
c)
d)
e)
tan t
1  sec t

simplifies to
1  sec t
tan t
2csct
2sect
2cot t
2 tan t
2sint
12. Which one of the following is an odd function?
3cos x
a) f ( x)  2
x tan x  csc x
b) f ( x)  x3  tan 2 x
1  x cos x
c) f ( x) 
sin x  tan x
x2
d) f ( x) 
3  cos x
e) f ( x)  x3 csc x  1
13. If f ( x)  3cos x and g ( x)  sin x  tan x , then
a) f ( x) is an even function and g ( x ) is an odd function.
b) both f ( x) and g ( x) are even functions.
c) f ( x) is an odd function and g ( x ) is an even function.
d) f ( x) is an even function and g ( x ) is neither an odd nor an even function.
e) both f ( x) and g ( x) are odd functions.
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