# Assignments Class 11 Mathematics Trigonometric Functions

Please refer to Assignments Class 11 Mathematics Trigonometric Functions Chapter 3 with solved questions and answers. We have provided Class 11 Mathematics Assignments for all chapters on our website. These problems and solutions for Chapter 3 Trigonometric Functions Class 11 Mathematics have been prepared as per the latest syllabus and books issued for the current academic year. Learn these solved important questions to get more marks in your class tests and examinations.

## Trigonometric Functions Assignments Class 11 Mathematics

Question. If sin θ + cos θ = 1, then sin θ cos θ =
(a) 0
(b) 1
(c) 2
(d) 1/2

A

Question. The solution of sin x = −√3/2 is
(a) x = nπ + (–1)n 4π/3 ,where n ∈ Z
(b) x = nπ + (–1)n 2π/3 , where n ∈ Z
(c) x = nπ + (–1)n 3π/3 , where n ∈ Z
(d) None of the above

A

Question. Radian measure of 40° 20′ is equal to
(d) None of these

B

Question. If sin A = 3/5 and A is in first quadrant, then the values of sin 2A, cos 2A and tan 2A are
(b) 1/25, 7/25, 1/7
(c) 24/25 , 1/25 , 24/7
(d) 1/25 , 24/25 , 1/24

A

Question. If sin θ + cos θ = 1, then the general value of θ is
(a) 2nπ
(b) nπ + (–1)n – π/4 – π/4
(c) 2nπ + π/2
(d) (2n – 1) + π/4

B

Question. Match the following in column-I with the given in column-II.

Codes:
A B C D
(a) 2 4 1 3
(b) 2 1 4 3
(c) 3 1 4 2
(d) 3 4 1 2

A

Question. The number of values of x in the interval [0,3π] satisfying the equation 2sin2 x + 5 sin x – 3 = 0 is
(a) 4
(b) 6
(c) 1
(d) 2

A

Question. A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
(a) 50°
(b) 210°
(c) 100°
(d) 60°

B

Question. Value of cos(3π/2+x) cos (2π+x)[cot(3π/2–x) + cot (2π+x)] is
(a) 0
(b) 1
(c) 2
(d) 3

B

Question. If 0 < θ < 360°, then solutions of cos θ = – 1/2 are
(a) 120º, 360º
(b) 240º, 90º
(c) 60º, 270º
(d) 120º, 240º

D

Question. If 2 sinα/{1+cosα+sinα} = y, then {1– cosα+sinα }/1+ sinα =
(a) 1/y
(b) y
(c) 1 – y
(d) 1 + y

B

Question. The degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm as shown in figure, is (Use π = 22/7)

(a) 12° 30′
(b) 12° 36′
(c) 11° 36′
(d) 11°12′

B

Question. If tan θ = a/b, then b cos 2θ + a sin 2θ is equal to
(a) a
(b) b
(c) a/b
(d) None of these

B

Question. If tan θ + tan 2θ + √3 tan θ tan 2θ = √3, then
(a) θ = (6n + 1) π/18 , ∀ n ∈ I
(b) θ = (6n + 1) π/9, ∀ n ∈ I
(c) θ = (3n + 1) π/9, ∀ n ∈ I
(d) θ = (3n + 1) π/18

C

Question. cosec A – 2 cot 2A cos A =
(a) 2 sin A
(b) sec A
(c) 2 cos A cot A
(d) None of these

A

Question. The value of cosec (–1410)° is equal to
(a) 1
(b) 2
(c) 1/2
(d) None of these

B

Question. The value of 3 sin π/6 sec π/3 – 4 sin 5π/6 cot π/4 is equal to
(a) 2
(b) 1
(c) 3
(d) 4

B

Question. Value of sin 47° + sin 61° – sin 11° – sin 25° is
(a) cos 7º
(b) sin 7º
(c) sin 61º
(d) –sin 25º

A

Question. What is the value of sin 5π/12 ?
(a) √3+1/2
(b) √6 + √2 /4
(c) √3+√2/4
(d) √6+1/2

B

Question. If sin A/sin B = m and cos A/cos B = n, then the value of tan B; n2 < 1 < m2, is

B

Question. If 4 sin2 θ + 2(√3 + 1) cos θ = 4 + √3, then the general value of θ is
(a) 2nπ ± π/3
(b) 2nπ + π/4
(c) nπ ± π/3
(d) nπ – π/3

A

Question. 1/4[√3 cos 23° – sin 23°] =
(a) cos 43°
(b) cos 7°
(c) cos 53°
(d) None of these

D

Question. [Use π = 22/7]

Codes:
A B C D
(a) 3 4 2 1
(b) 1 4 2 3
(c) 3 4 1 2
(d) 2 4 1 3

C

Question. If sin 5x + sin 3x + sinx = 0 and 0 ≤ x ≤ π/2, then value of x is
(a) π/2
(b) π/6
(c) π/3
(d) π/4

C

Question. The value of cot (–15π/4) is
(a) –1/3
(b) 1
(c) 3
(d) – 3

B

Question. If sec 4θ – sec 2θ = 2, then the general value of θ is
(a) (2n + 1)π/4
(b) (2n + 1)π/10
(c) nπ +π/2 or nπ/5 + π/10
(d) (2n + 1)π/2

C

Question. The value of cos2 π/12 + cos2 π/4 + cos2 5π/12 is
(a) 3/2
(b) 2/3
(c) 3 + √3/2
(d) 2/3 + √3

A

Question. The value of (1+cosπ/6)(1+cosπ/3)(1+cos2π/3)(1+cos7π/6) is m/16 . Value of m is
(a) 1
(b) 2
(c) 3
(d) 8

C

Question. If none of the angles x, y and (x + y) is a multiple of π, then
(a) cot (x + y) = cot x.cot y – 1/cot y + cot x
(b) cot (x – y) = cot x.cot y+1/cot y – cot x
(c) (a) and (b) are true
(d) (a) and (b) are not true

C

Question. A wheel rotates making 20 revolutions per second. If the radius of the wheel is 35 cm, what linear distance does a point of its rim travel in three minutes? (Take π = 22/7)
(a) 7.92 km
(b) 7.70 km
(c) 7.80 km
(d) 7.85 km

A

Question. The solution of tan 2θ tan θ = 1 is
(a) 2nπ+π/3
(b) nπ+π/4
(c) 2nπ–π/6
(d) (2n+1)π/6

D

Question. If sin x = –2√6/5 and x lies in III quadrant, then the value of cot x is 1/m√6 . Value of m is
(a) 1
(b) 2
(c) 3
(d) 5

B

Question. The value of sin 31π/3 is
(a) √3/2
(b) –√3/2
(c) –1/√2
(d) 1/√2

A

Question. Value of (1+cosπ/8)(1+cos3π/8)(1+cos5π/8)(1+cos7π/8) is
(a) 1/8
(b) 3/4
(c) 2/3
(d) 5/8

D

Question. The value of tan 75° – cot 75° is equal to
(a) 2√3
(b) 2+√3
(c) 2– √3
(d) 1

A

Question. The value of tan 3A – tan 2A – tan A is equal to
(a) tan 3A tan 2A tan A
(b) –tan 3A tan 2A tan A
(c) tan A tan 2A – tan 2A tan 3A – tan 3A tan A
(d) None of these

A

Question. If tan A = 1/2 ,tan B = 1/3 , then tan(2A + B) is equal to
(a) 1
(b) 2
(c) 3
(d) 4

C

Question. If cos A = 4/5 , cosB = 12/13 , 3π/2 , < A, B < 2π , the value of the cos (A + B) is
(a) 65/33
(b) 33/65
(c) 30/65
(d) 65/30

B

Question. cos (A + B). cos ( A – B) is given by:
(a) cos2 A – cos2B
(b) cos( A2 – B2)
(c) cos2A – sin2B
(d) sin2A – cos2B

C

Question. 1 + sin A – cos A/1 + sin A + cos A =
(a) sinA/2
(b) cosA/2
(c) tanA/2
(d) cotA/2

C

Question. If cot θ + cot(π/4 + θ) = 2, then the general value of θis
(a) 2nπ ± π/6
(b) 2nπ ± π/3
(c) nπ ± π/3
(d) nπ ± π/6

D

Question. If √2 sec θ + tan θ = 1, then the general value of θ is
(a) nπ + 3π/4
(b) 2nπ + π/4
(c) 2nπ – π/4
(d) 2nπ ± π/4

C

Question. If m sin θ = n sin (θ + 2α), then tan (θ + α) . cot α is equal to
(a) m + n/m – n
(b) m – n/m + n
(c) m + n/mn
(d) m – n/mn

A

Question. If y = 2sinα/1+cosα+sinα, then value of 1–cosα+sinα /1+sinα is
(a) y/3
(b) y
(c) 2y
(d) 3/2y

B

Question. If sinθ = 24/25 and 0° < θ??< 90° then what is the value of sin(θ/2)?
(a) 12/25
(b) 7/25
(c) 3/5
(d) 4/5

C

Question. If tan A = 1/2 and tan B = 1/3 , then value of A + B is
(a) π
(b) π/6
(c) π/2
(d) π/4

D

Question. The general value of θ satisfying the equation tan θ + tan(π/2–θ) = 2, is
(a) nπ ± π/4
(b) nπ + π/4
(c) 2nπ ± π/4
(d) nπ + (–1)nπ/4

B

Question. If √3 tan 2θ + √3 tan 3θ + tan 2θ tan 3θ = 1, then the general value of θ is
(a) nπ ± π/5
(b) (n+1/6)π/5
(c) (2n±1/6) π/5
(d) (n+1/3)π/5

B

Question. The large hand of a clock is 42 cm long. How much distance does its extremity move in 20 minutes?
(a) 88 cm
(b) 80 cm
(c) 75 cm
(d) 77 cm

A

Question. Which among the following is/are correct?
(a) The angle is called negative, if the rotation is clockwise
(b) The angle is called positive, if the rotation is anti-clockwise
(c) The amount of rotation performed to get the terminal side from the initial side is called the measure of an angle
(d) All the above are correct

D

Question. If cot θ + tan θ = 2 cosec θ, the general value of θ is
(a) nπ ± π/3
(b) nπ ± π/6
(c) 2nπ ± π/3
(d) 2nπ ± π/6

C

Question. The value of cot 54°/tan 36° + tan 20°/ cot 70° is
(a) 2
(b) 3
(c) 1
(d) 0

A

Question. The value of cosec (–1410)° is equal to
(a) 1
(b) 1/2
(c) 2
(d) None of these

C

Question. The value of tan 20° + 2 tan 50° – tan 70° is equal to
(a) 1
(b) 0
(c) tan 50°
(d) None of these

B

Question. The expression cos10π/13 + cos8π/13 + cos3π/13 + cos5π/13 is equal to
(a) –1
(b) 0
(c) 1
(d) None of these

B

Question. If 1 + cot θ = cosec θ, then the general value of θ is
(a) nπ + π/2
(b) 2nπ – π/2
(c) 2nπ + π/2
(d) 2nπ ± π/2

C

Question. The value of tan2θ sec2θ (cot2θ – cos2θ) is
(a) 0
(b) 1
(c) –1
(d) 1/2

B

Question. The most general value of θ satisfying the equation
cosθ = 1/√2/and tanθ = – 1 is
(a) 2nπ–7.π/4
(b) nπ–π/4
(c) nπ+π/2
(d) 2nπ+7π/4

D

Question. Value of tan15°. tan45° tan75° is
(a) 0
(b) 1
(c) √3/2
(d) –1