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

Questions
1 Find all angles θ such that -2π < θ < 2π and cos θ = √2 / 2
A {-7 π / 4, - π / 4 , π / 4 , 7 π / 4}
B {- π / 4, - 3 π / 4 , π / 4 , 3 π / 4}
C {-5 π / 4, π / 4 , 3 π / 4}
D {π / 4 , π / 4 , 3 π / 4}

Answer:{-7 π / 4, - π / 4 , π / 4 , 7 π / 4}
2 If sin t = 1/5 and 0 < t < π/ 2, then cos (4 t) = ?
A 0.3464
B 0.8
C 0.6928
D - 0.6928

Answer:0.6928
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3 If cos t = 1/3 and 3π /2 < t < 2π in quadrant IV, then sin (4 t) = ?
A 8 √2 / 3
B - 8 √2 / 3
C - 56 √2 / 243
D 56 √2 / 81

Answer:56 √2 / 81
4 If cos t = 3/4, and sin t < 0, then sin (3 t) = ?
A √7 / 16
B - 5 √7 / 16
C - 3 √7 / 4
D 5 √7 / 16

Answer:- 5 √7 / 16
5 If tan x = 5, then tan (2 x) = ?
A 10
B - 5 / 12
C 1 / 10
D 5 / 12

Answer:- 5 / 12
6 If cos t = 0.8, then cos (2 t) = ?
A 0.28
B 0.4
C 1.0
D 1.6

Answer:0.28
7 If sin t = 0.6 and cot t > 0, then sin (2 t) = ?
A - 0.96
B 0.48
C 0.96
D - 0.48

Answer:0.96
8 Which of the following is not correct?
A sin(x) = -sin(-x)
B sec(-t) = sec(t)
C sin(π + x) = sin(x)
D cos(π - x) = -cos(x)

Answer:sin(π + x) = sin(x)
9 Which of the following is not the same as tan(t)?
A - tan(-t)
B tan(t + 2π)
C tan(t + π)
D tan(t + π / 2)

Answer:tan(t + π / 2)
10 If sin(-t) = 0.54, what is - sin(t) ?
A 0.54
B -0.54
C - 0.46
D 0.46

Answer:0.54
11 If cos(-t) = 0.34, what is cos(t) ?
A -0.34
B 0.66
C 0.34
D - 0.66

Answer:0.34
12 If 0 < t < π/2 and sin t = 0.65, what is sin(t + π) ?
A -0.65
B 0.65
C 0.35
D 0.76

Answer:-0.65
13 cos(x) + cos(π - x) =?
A 2 cos(x)
B cos(x) - sin(x)
C cos(x) + sin(x)
D 0

Answer: 0
14 If tan(t) = 13, then cot(-t) =?
A 13
B 1 / 13
C - 1 / 13
D - 13

Answer:- 1 / 13
15 If 0 < t < π / 2 and sin t = 0.35, then cos(t + π) =?
A 0.94
B -0.94
C 0.81
D -0.81

Answer: -0.94
16 If point (a , b) is on the Unit Circle associated with the rotation t, then the point on the Unit circle associated with rotation t + π / 2, has the following coordinates
A (b , a)
B (-b , a)
C (-b , -a)
D (-a , b)

Answer:(-b , a)
17 If point (a , b) is on the Unit Circle associated with the rotation t and point (c , d) is also on the Unit circle associated with rotation t + π, then which of the following is correct?
A c = - a and d = - b
B c = - a and d = b
C c = a and d = b
D c = a and d = - b

Answer:c = - a and d = - b
18 If point (a , b) is on the Unit Circle associated with the rotation t, which of the following is not correct?
A sin(t) = b
B cos(t) = a
C sin(-t) = - a
D cos(-t) = - a

Answer:cos(-t) = - a
19 Find the point on the Unit Circle associated with the angle 5π/3
A (1 / 2 , 1 / 2)
B (-√3 / 2 , 1/2)
C (1 / 2 , -√3 / 2)
D (-√3 / 2 , -1/2)

Answer: (1 / 2 , -√3 / 2)
20 Find the point on the Unit Circle associated with the rotation -9π/2
A (0 , -1)
B (0 , 1)
C (1 , 0)
D (-1 , 0)

Answer: (-1 , 0)

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