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NCERT Solutions for class 11 Maths | Chapter 3 - Trigonometric Functions

Questions
1 A point is in Quadrant-III and on the Unit Circle. If its x-coordinate is -4 / 5, what is the y-coordinate of the point?
A 3 / 5
B -3 / 5
C -2 / 5
D 5 / 3

Answer:-3 / 5
2 Which of the following points is in the unit circle?
A (-√2 / 2 , -√2 / 2)
B (√2 / 3 , -√2 / 3)
C (1 / 2 , 1 / 2)
D (3 / 2 , 2 / 3)

Answer:(-√2 / 2 , -√2 / 2)
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3 What is the amplitude of f(x) = sin(x) + cos(x)?
A √2
B √2 / 2
C 2 √2
D 2

Answer:√2
4 What is the period of f(x) = 0.5 sin(x) cos(x)?
A 0.5
B 2 π
C π / 2
D π

Answer:π / 2
5 What is the amplitude of f(x) = 4 sin(x) cos(x)?
A 4
B 3
C 2
D 1

Answer:2
6 What is the range of the function f(x) = - 6 cos(π x - π/2) + 2?
A [-6 , 6]
B [-4 , 8]
C [0 , 8]
D [-6 , 0]

Answer:[-4 , 8]
7 What is the phase shift of the function f(x) = 7sin(2x - π / 3)?
A π / 3
B π / 6
C - π / 6
D - π / 3

Answer:π / 6
8 What is the range of the function f(x) = - 4 cos(2x - 3)?
A (0 , 4)
B [0 , 4]
C (-4 , 4)
D [-4 , 4]

Answer:[-4 , 4]
9 Which of the following functions has the greatest period?
A f(x) = 20 sin(2x-π/2)
B f(x) = - sin(πx)
C f(x) = 2 sin(0.1 x)
D f(x) = - sin(0.1 π x)

Answer:f(x) = 2 sin(0.1 x)
10 What is the period of the trigonometric function given by f(x) = 2 sin(5 x)?
A π / 5
B 2 π / 5
C 5 π
D π

Answer:2 π / 5
11 If y = cos x, then what is the maximum value of y?
A 1
B -1
C π
D 2π

Answer:1
12 The value of (sin7x + sin5x) /(cos7x + cos5x) + (sin9x + sin3x) / (cos9x + cos3x) is
A tan6x
B tan6x
C tan6x
D tan6x

Answer:tan6x
13 If a*cos x + b*cos x = c, then the value of (a*sin x - b*cos x)2 is
A a2 + b2 + c2
B a2 - b2 - c2
C a2 - b2 + c2
D a2 + b2 - c2

Answer: a2 + b2 - c2
14 The value of cos 4A - cos 4B is
A (cos A - cos B)*(cos A + cos B)*(cos A - sin B)*(cos A + sin B)
B (cos A - cos B)*(cos A + cos B)*(cos A - sin B)*(cos A + sin B)
C (cos A - cos B)*(cos A + cos B)*(cos A - sin B)*(cos A + sin B)
D (cos A - cos B)*(cos A + cos B)*(cos A - sin B)*(cos A + sin B)

Answer:(cos A - cos B)*(cos A + cos B)*(cos A - sin B)*(cos A + sin B)
15 The value of cos(π/7) * cos(2π/7) * cos(4π/7) is
A -1/2
B -1/4
C -1/6
D -1/8

Answer:-1/8
16 tan2 θ = 1 - a2 then the value of sec θ + tan3 θ * cosec θ is
A (2 - a2 )
B (2 - a2 )1/2
C (2 - a2 )3/2
D None of these

Answer:(2 - a2 )3/2
17 If tan2 θ = 1 - e2 , then the value of sec θ + tan3 θ * cosec θ is
A 2 - e2
B (2 - e2 )1/2
C (2 - e2 )2
D (2 - e2 )3/2

Answer:(2 - e2 )3/2
18 If tan(A + B) = x and tan(A - B) = y then the value of tan 2A is
A (x + y)/(1 - xy)
B (x - y)/(1 + xy)
C (x + y)/2xy
D None of these

Answer:(x + y)/(1 - xy)
19 If tan(A + B) = x and tan(A - B) = y then the value of tan 2B is
A (x + y)/(1 - xy)
B (x - y)/(1 + xy)
C (x + y)/2xy
D (x - y)/2xy

Answer: (x - y)/(1 + xy)
20 If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is
A π/3
B π/2
C 2π/3
D 3π/2

Answer:2π/3

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