Maths · Sets and functions · chapter 3 of 14

Class 11 Maths Chapter 3: Trigonometric Functions MCQs with answers

10 multiple-choice questions on Trigonometric Functions, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
The radian measure of 135° is
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Answer: (b) 3π/4

Radian measure = (π/180) × 135 = 135π/180 = 3π/4. 2π/3 is 120° and 5π/6 is 150°.

Question 2
An angle of 5π/12 radian, written in degrees, is
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Answer: (c) 75°

Degree measure = (180/π) × (5π/12) = 5 × 15 = 75°. 150° doubles it by using 360° for π.

Question 3
A sector of a circle of radius 7 cm has a perimeter (two radii and the arc) of 25 cm. The angle of the sector, in radians, is
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Answer: (a) 117

The arc is 25 − 2 × 7 = 11 cm, so θ = l/r = 11/7 radian. 25/7 forgets to take away the two radii; 18/7 takes away only one; 11/14 divides by the diameter.

Question 4
At 4 o'clock, the smaller angle between the hour hand and the minute hand of a clock, in radians, is
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Answer: (d) 2π/3

The 12 hour marks divide 360° into 30° each. At 4 o'clock the hands are 4 marks apart: 4 × 30° = 120° = (π/180) × 120 = 2π/3. 4π/3 is the larger angle, 240°.

Question 5
If sin x > 0 and tan x < 0, then x lies in the
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Answer: (b) second quadrant

sin x is positive in quadrants I and II; tan x is negative in quadrants II and IV. Both hold only in the second quadrant.

Question 6
The value of 4 sin (π/2) − 3 cos π + 2 cos (3π/2) is
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Answer: (c) 7

sin (π/2) = 1, cos π = −1, cos (3π/2) = 0, so the value is 4 + 3 + 0 = 7. Taking cos π as 1 gives 1.

Question 7
Which of the following is equal to sin 20°?
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Answer: (a) sin 380°

380° = 360° + 20°, and sin (2nπ + x) = sin x, so sin 380° = sin 20°. sin (−20°) = −sin 20°, sin 200° = sin (180° + 20°) = −sin 20°, and cos 20° = sin 70°.

Question 8
sec x is not defined at
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Answer: (c) x = π/2

sec x = 1/cos x is defined only where cos x ≠ 0, i.e. x ≠ (2n + 1)π/2. cos (π/2) = 0; at 0, π and 2π cos x is 1 or −1.

Question 9
Which of the following can never be a value of cos x for a real number x?
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Answer: (d) π/3

For every real x, −1 ≤ cos x ≤ 1. π/3 ≈ 1.047 is greater than 1; the other three lie in [−1, 1] (cos π = −1).

Question 10
If tan x = 12, then sin 2x is
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Answer: (d) 45

sin 2x = 2 tan x/(1 + tan² x) = 1/(1 + 1/4) = 4/5. 4/3 is tan 2x and 3/5 is cos 2x.

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