Download ExamView - A2.A.58.ReciprocalTrigonometricRelatonships.tst

Regents Exam Questions
A2.A.58: Reciprocal Trigonometric Relationships
Name: ________________________
www.jmap.org
A2.A.58: Reciprocal Trigonometric Relationships: Know and apply the co-function and
reciprocal relationships between trigonometric ratios
1 The expression
1)
2)
3)
4)
sin 
cos 
sin 
cos 
cos 
sin 
2 The expression
6 The expression cot   sec  is equivalent to
cos 
1)
sin 2 
sin 
2)
cos 2 
3) csc 
4) sin 
7 The expression (tan )(csc ) is equivalent to
1) cos 
2) sec 
3) csc 
4) csc  cot 
8 Expressed in simplest form, csc   tan   cos  is
equivalent to
1) 1
2) sin 
3) cos 
4) tan 
sec 
is equivalent to
csc 
tan 
is equivalent to
sec 
cos 2 
sin 
sin 
2)
cos 2 
3) cos 
4) sin 
3 For all values of  for which the expression is
cot 
defined,
is equivalent to
csc 
1) cos 
2) sin 
3) csc 
4) tan 
4 For all values of  for which the expression is
csc 
defined,
is equivalent to
sec 
1) cos 
2) sin 
3) cot 
4) tan 
1
5 If sin x  , a  0, which statement must be true?
a
1) csc x  a
1
2) csc x  
a
3) sec x  a
1
4) sec x  
a
1)
9 The expression (sec 2 )(cot 2 )(sin ) is equivalent
to
1) sin 
2) cos 
3) csc 
4) sec 
10 The expression cos y(csc y  sec y) is equivalent to
1) cot y  1
2) tan y  1
3) 1  tany
4) cos y
11 The expression cos (sec   cos ) is equivalent to
1) 1
2) sin 
3) sin 2 
4) cos 2 
12 The expression sin (cot   csc ) is equivalent to
1)
2)
3)
4)
1
cos   sin2 
2cos 
sin 
cos   1
Regents Exam Questions
A2.A.58: Reciprocal Trigonometric Relationships
Name: ________________________
www.jmap.org
13 The expression 1  sec x is equivalent to
1) tanx
cos x  1
2)
cos x
sin x  1
3)
sinx
tan x
4)
sec x  1
14 For all values of x for which the expressions are
defined, sec x  tan x is equivalent to
1) 1
2) cos x  cot x
1  sinx
3)
cos x
4)
cos x  sin 2 x
sin x cos x
15 The expression sin A 
1)
2)
3)
4)
3)
sin 2 x  cos 2 x
is equal to
cos x
4)
7
4
4
7
ÊÁ
ˆ
ÁÁ
3 ˜˜˜˜
Á
˜
22 Evaluate: csc ÁÁ Arc sin
ÁÁ
2 ˜˜˜
Ë
¯
csc x
sec x
cos x  tanx
sin x  cos x  tanx
17 The expression
1)
2)
3)
4)
cos 2 A
is equivalent to
sinA
1
sin A
sec A
csc A
16 The expression
1)
2)
3)
4)
19 The expression sec 2   tan 2  is equal to
1) 1
2) 0
3) sin 2 
1
4)
cos 2 
20 If csc   2, what is the value of sin  ?
1) 2
2) 2
1
3) 
2
1
4)
2
ÊÁ
3 ˆ˜
21 What is the value of csc ÁÁÁ Arc sin ˜˜˜ ?
ÁË
4 ˜¯
3
1)
4
4
2)
3
sin 2   cos 2 
is equivalent to
1  sin 2 
cos 2 
sin 2 
sec 2 
csc 2 
ÁÊ
5 ˜ˆ
23 What is the value of sec ÁÁÁÁ Arc cos ˜˜˜˜ ?
7¯
Ë
18 The expression sec 2 x  csc 2 x is equivalent to
1) 1
1
2)
cos x sinx
3) cos 2 x sin 2 x
1
4)
2
cos x sin 2 x
2
ID: A
A2.A.58: Reciprocal Trigonometric Relationships: Know and apply the co-function and
reciprocal relationships between trigonometric ratios
Answer Section
1 ANS: 3
REF: 010402b
2 ANS: 4
REF: 010508b
3 ANS: 1
4 ANS: 3
5 ANS: 1
1
sin x 
.
csc x
REF: 068920siii
REF: 080318siii
REF: 060904b
6 ANS: 3
7
8
9
10
11
12
13
REF:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
010915b
2
1
3
1
3
4
2
REF: 080813b
14 ANS: 3
REF:
REF:
REF:
REF:
REF:
REF:
010122siii
069921siii
010427siii
068731siii
019630siii
060018siii
REF: 068623siii
1
ID: A
15 ANS: 4
REF: 060720b
16 ANS: 2
REF: 089316siii
17 ANS: 3
1
sin 2   cos 2 

 sec 2 
2
2
cos 
1  sin 
REF:
18 ANS:
19 ANS:
20 ANS:
061123a2
4
1
3
REF: 089428siii
REF: 060220siii
REF: 080703b
21 ANS: 2
REF: 080817b
22 ANS:
2
3
REF: 069410siii
23 ANS:
7
5
REF: 010315siii
2