Download A2.A.56: Determining Trigonometric Functions 2: Know the exact

Regents Exam Questions
A2.A.56: Determining Trigonometric Functions 2
Name: ________________________
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A2.A.56: Determining Trigonometric Functions 2: Know the exact and approximate values of the
sine, cosine, and tangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles
x
1 If f(x) = cos x + tan , then f(π) is
3
3 +3
3
1)
3 −3
3
3 +1
3 −1
2)
3)
4)
2 At x =
1)
2)
3)
4)
 π 
5 If f(x) = sin2 x, then f   equals
2
1) 1
3
2)
4
1
3)
2
1
4)
4
1
2
3
0
π
2
6 If f(x) = sinx + cos 2x, then f(π) is
1) 1
2) 2
3) 0
4) −1
, the difference 2sinx − cos 2x is
7 The value of sin
 π 
3 The value of cos   is
4
2
1)
2)
3)
4)
1
1
2
1
4
0
4 The value of sin
1)
2)
3)
4)
3
2
π
6
+ tan
π
4
is
1)
−
2)
1
2
3)
−
4)
0
3 +2
2
2
3+
2
3
cos π is
3
2
1
2
8 What is the value of tan
1)
1+
π
2)
2
3)
4)
2
1
3 +3
3
3 −3
3
3 −1
3 +1
π
3
+ cos π ?
Regents Exam Questions
A2.A.56: Determining Trigonometric Functions 2
Name: ________________________
www.jmap.org
x
9 If f(x) = sin , find f(π) equals
4
1) 1
1
3
2)
2
1
3)
2
2
1
4)
2
10 The value of cos
1
2
1)
1
2)
1
2
3)
−
4)
−1
π
3
− sin
13 The numerical value of sin
1)
3π
is
2
2)
2
2
3)
−1 +
4)
−1
2
2
2
2
 π 
14 If f(x) = sin2x + cos x, what is f   ?
 4 
1)
1
2
1+
3π
π
+ cos is
2
4
2)
1
2
3)
4)
 π 
11 If f(x) = cos 3x + sinx, then f   equals
2
1) 1
2) 2
3) −1
4) 0
1+
2
2
1+
3
0
2
2
15 Find the value of sin2
16 Find the value of sin
 3π 
 
 − cos  π  is
12 The value of sin

3
 2 
 
1
1) −1
2
1
2) 1
2
1
3)
2
1
4) −
2
π
3
π
2
.
− cos
3π
.
2
17 If f x = 3cos x, find the numerical value of f π  .
 π 
18 If f(x) = 2cos x, find f   .
3
19 What is the numerical value of the product



 tan π   cos π  ?



4  
3 

2
Regents Exam Questions
A2.A.56: Determining Trigonometric Functions 2
Name: ________________________
www.jmap.org
x
20 If f(x) = sinx + cos , find f(2π).
2
 π 
31 If f(x) = sin2x + cos x, find the value of f   .
2
 π 
21 If f x = cos 2x, find f   .
 2 
 π 
32 If f(x) = tanx, evaluate f   .
4
22 If f(x) = cos x + sinx, find the value of f(x) when
3π
.
x=
2
23 If f(θ) = tan θ − 2cos θ , find f(π).
24 Evaluate: cos
π
2
+sin
3π
2
x
25 If f(x) = 4sin , find f(π).
3
26 If f(x) = sin2 x + cos 2 x, find f(
π
4
).
 π 
27 If f x = 2sin2 x + sinx + 1, find the value of f   .
6
 π 
28 If f x = sin3x + cos x, what is f   ?
2
1
29 If f x = sin x + 2cos x, evaluate f(π).
2
 π 
30 If f(x) = 2cos 2 x + sinx − 1, find the value of f   .
2
3
ID: A
A2.A.56: Determining Trigonometric Functions 2: Know the exact and approximate values of the
sine, cosine, and tangent of 0º, 30º, 45º, 60º, 90º, 180º, and 270º angles
Answer Section
1
2
3
4
5
6
7
8
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11
12
13
14
15
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
ANS:
3
4
4
3
2
1
1
1
1
3
3
1
1
1
3
1
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
PTS:
2
2
2
2
2
2
2
2
2
2
2
2
2
2
PTS: 2
16 ANS:
1
REF: 018402siii
PTS: 2
17 ANS:
−3
REF: 068415siii
PTS: 2
18 ANS:
1
REF: 018511siii
PTS: 2
19 ANS:
1
2
REF: 088711siii
PTS: 2
20 ANS:
−1
REF: 068814siii
PTS: 2
REF: 010408siii
REF:
REF:
REF:
REF:
REF:
REF:
REF:
REF:
REF:
REF:
REF:
REF:
REF:
REF:
068129siii
068437siii
088426siii
068528siii
089322siii
068924siii
088935siii
089025siii
019420siii
069531siii
069718siii
089722siii
010017siii
080317siii
1
ID: A
21 ANS:
−1
PTS: 2
22 ANS:
−1
REF: 019012siii
PTS: 2
23 ANS:
2
REF: 069406siii
PTS: 2
24 ANS:
−1
REF: 089936siii
PTS: 2
25 ANS:
2 3
REF: 019507siii
PTS: 2
26 ANS:
1
REF: 069510siii
PTS: 2
27 ANS:
2
REF: 019606siii
PTS: 2
28 ANS:
−1
REF: 019812siii
PTS: 2
29 ANS:
−1
REF: 019905siii
PTS: 2
30 ANS:
0
REF: 069909siii
PTS: 2
31 ANS:
0
REF: 010011siii
PTS: 2
32 ANS:
1
REF: 060002siii
PTS: 2
REF: 010102siii
2