Trigonometric Functions MCQ Questions for Class 11 and JEE

Practice Class 11 Maths Chapter 3 Trigonometric Functions MCQ Questions with Answers to strengthen your understanding of one of the most important chapters in algebra and IIT JEE preparation. This chapter covers angles and their measurement, degree and radian conversion, trigonometric ratios, standard values, signs of trigonometric functions in different quadrants, identities, domain and range, and trigonometric equations.

These Trigonometric Functions MCQs for Class 11 are designed to help students revise NCERT Class 11 concepts, apply formulas correctly, and improve speed and accuracy in objective-type questions. Each question includes four options, the correct answer, and a detailed explanation so that students can understand the method instead of only memorising the answer.

This set of Class 11 Maths Chapter 3 MCQ Questions is useful for CBSE exams, NCERT revision, online tests, JEE Foundation, and JEE Main preparation. Students can also use the Trigonometric Functions MCQ Questions with Answers PDF for offline practice and quick revision before exams.

What are Trigonometric Functions?

Trigonometric functions are functions of an angle. The six main trigonometric functions are:

• sin x
• cos x
• tan x
• cot x
• sec x
• cosec x

In Class 11, trigonometric functions are defined using the unit circle. If a point P(a, b) lies on the unit circle and makes an angle x with the positive x-axis, then:

cos x = a
sin x = b

This gives the important identity:

sin²x + cos²x = 1

Trigonometric functions are used in Maths and Physics to study waves, oscillations, rotations, circular motion and periodic behaviour.

Important Trigonometric Formulas for Class 11 and JEE

Also Check: Trigonometric Formulas for Class 11 and JEE.

Standard Trigonometric Values Table

Signs of Trigonometric Functions in Quadrants

A simple memory rule is ASTC:

• A: All positive in Quadrant I
• S: Sine positive in Quadrant II
• T: Tangent positive in Quadrant III
• C: Cosine positive in Quadrant IV

Trigonometric Functions MCQ Questions with Answers

MCQs on Angles, Degree and Radian Measure

Q1. One complete revolution is equal to:

(a) π radians
(b) 2π radians
(c) π/2 radians
(d) 3π/2 radians

Answer: (b) 2π radians

Solution: One complete revolution is 360°. Since π radians = 180°, therefore 360° = 2π radians.

Q2. The radian measure of 180° is:

(a) π/2
(b) π
(c) 2π
(d) 3π

Answer: (b) π

Solution: We know that 180° = π radians.

Q3. The radian measure of 90° is:

(a) π/6
(b) π/4
(c) π/3
(d) π/2

Answer: (d) π/2

Solution:
Radian = (π/180) × Degree
= (π/180) × 90 = π/2.

Q4. The degree measure of π/3 radians is:

(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer: (c) 60°

Solution:
Degree = (180/π) × π/3 = 60°.

Q5. The radian measure of 45° is:

(a) π/2
(b) π/3
(c) π/4
(d) π/6

Answer: (c) π/4

Solution:
45° = 45 × π/180 = π/4.

Q6. The degree measure of 5π/6 is:

(a) 120°
(b) 135°
(c) 150°
(d) 180°

Answer: (c) 150°

Solution:
Degree = (180/π) × 5π/6 = 150°.

Q7. If an angle is measured anticlockwise, it is considered:

(a) Negative
(b) Positive
(c) Zero
(d) Undefined

Answer: (b) Positive

Solution: In standard convention, anticlockwise rotation gives a positive angle.

Q8. If an angle is measured clockwise, it is considered:

(a) Positive
(b) Negative
(c) Acute
(d) Right angle

Answer: (b) Negative

Solution: Clockwise rotation from the initial side gives a negative angle.

Q9. The radian measure of 270° is:

(a) π/2
(b) π
(c) 3π/2
(d) 2π

Answer: (c) 3π/2

Solution:
270° = 270 × π/180 = 3π/2.

Q10. The degree measure of 7π/6 is:

(a) 180°
(b) 210°
(c) 240°
(d) 270°

Answer: (b) 210°

Solution:
Degree = (180/π) × 7π/6 = 210°.

MCQs on Arc Length and Circular Measure

Q11. If an arc of length l subtends an angle θ at the centre of a circle of radius r, then:

(a) l = θ/r
(b) l = rθ
(c) l = r/θ
(d) l = r²θ

Answer: (b) l = rθ

Solution: The arc length formula is l = rθ, where θ is measured in radians.

Q12. If r = 7 cm and θ = π/2, then arc length is:

(a) 7π/2 cm
(b) 14π cm
(c) π/14 cm
(d) 7/π cm

Answer: (a) 7π/2 cm

Solution:
l = rθ = 7 × π/2 = 7π/2 cm.

Q13. If l = 20 cm and r = 10 cm, then θ is:

(a) 1 radian
(b) 2 radians
(c) 5 radians
(d) 10 radians

Answer: (b) 2 radians

Solution:
θ = l/r = 20/10 = 2 radians.

Q14. If radius is doubled and angle remains the same, arc length becomes:

(a) Half
(b) Double
(c) Same
(d) Zero

Answer: (b) Double

Solution: Since l = rθ, if r becomes 2r, then arc length also becomes double.

Q15. If a circle has radius 14 cm and angle π/3, then arc length is:

(a) 14π/3 cm
(b) 3π/14 cm
(c) 42π cm
(d) 7π cm

Answer: (a) 14π/3 cm

Solution:
l = rθ = 14 × π/3 = 14π/3 cm.

MCQs on Unit Circle and Quadrantal Angles

Q16. On the unit circle, if P(a,b) corresponds to angle x, then cos x is:

(a) a
(b) b
(c) a+b
(d) ab

Answer: (a) a

Solution: On the unit circle, cos x is the x-coordinate of point P.

Q17. On the unit circle, if P(a,b) corresponds to angle x, then sin x is:

(a) a
(b) b
(c) a−b
(d) a/b

Answer: (b) b

Solution: On the unit circle, sin x is the y-coordinate of point P.

Q18. The value of sin 0 is:

(a) 0
(b) 1
(c) −1
(d) Not defined

Answer: (a) 0

Solution: On the unit circle, at angle 0, the point is (1,0), so sin 0 = 0.

Q19. The value of cos 0 is:

(a) 0
(b) 1
(c) −1
(d) Not defined

Answer: (b) 1

Solution: At angle 0, the point on the unit circle is (1,0), so cos 0 = 1.

Q20. The value of sin π/2 is:

(a) 0
(b) 1
(c) −1
(d) Not defined

Answer: (b) 1

Solution: At π/2, the unit circle point is (0,1), so sin π/2 = 1.

Q21. The value of cos π is:

(a) 1
(b) 0
(c) −1
(d) Not defined

Answer: (c) −1

Solution: At π, the unit circle point is (−1,0), so cos π = −1.

Q22. The value of sin 3π/2 is:

(a) 1
(b) 0
(c) −1
(d) Not defined

Answer: (c) −1

Solution: At 3π/2, the unit circle point is (0,−1), so sin 3π/2 = −1.

Q23. The value of cos 2π is:

(a) 0
(b) 1
(c) −1
(d) Not defined

Answer: (b) 1

Solution: At 2π, the unit circle returns to (1,0), so cos 2π = 1.

Q24. Angles that are integral multiples of π/2 are called:

(a) Acute angles
(b) Obtuse angles
(c) Quadrantal angles
(d) Complementary angles

Answer: (c) Quadrantal angles

Solution: Angles such as 0, π/2, π, 3π/2 and 2π are quadrantal angles.

Q25. The point on the unit circle corresponding to π is:

(a) (1,0)
(b) (0,1)
(c) (−1,0)
(d) (0,−1)

Answer: (c) (−1,0)

Solution: At angle π, the terminal point lies on the negative x-axis.

MCQs on Standard Trigonometric Values

Q26. The value of sin 30° is:

(a) 1/2
(b) √3/2
(c) 1/√2
(d) √3

Answer: (a) 1/2

Solution: From the standard trigonometric table, sin 30° = 1/2.

Q27. The value of cos 60° is:

(a) 1/2
(b) √3/2
(c) 1/√2
(d) 1

Answer: (a) 1/2

Solution: From the standard trigonometric table, cos 60° = 1/2.

Q28. The value of tan 45° is:

(a) 0
(b) 1
(c) √3
(d) Not defined

Answer: (b) 1

Solution:tan 45° = sin 45°/cos 45° = 1.

Q29. The value of sin 60° is:

(a) 1/2
(b) √3/2
(c) 1/√2
(d) 0

Answer: (b) √3/2

Solution: From the standard value table, sin 60° = √3/2.

Q30. The value of cos 30° is:

(a) 1/2
(b) √3/2
(c) 1/√2
(d) 0

Answer: (b) √3/2

Solution: From the standard value table, cos 30° = √3/2.

Q31. The value of tan 60° is:

(a) 1/√3
(b) 1
(c) √3
(d) 0

Answer: (c) √3

Solution:
tan 60° = sin 60°/cos 60° = (√3/2)/(1/2) = √3.

Q32. The value of cot 45° is:

(a) 0
(b) 1
(c) √3
(d) Not defined

Answer: (b) 1

Solution:cot 45° = 1/tan 45° = 1.

Q33. The value of sec 60° is:

(a) 1
(b) 2
(c) √3
(d) 1/2

Answer: (b) 2

Solution:
sec 60° = 1/cos 60° = 1/(1/2) = 2.

Q34. The value of cosec 30° is:

(a) 1
(b) 2
(c) √3
(d) 1/2

Answer: (b) 2

Solution:
cosec 30° = 1/sin 30° = 1/(1/2) = 2.

Q35. The value of sin²30° + cos²30° is:

(a) 0
(b) 1
(c) 2
(d) √3

Answer: (b) 1

Solution: For every angle θ, sin²θ + cos²θ = 1.

MCQs on Signs of Trigonometric Functions

Q36. In the first quadrant, which trigonometric functions are positive?

(a) Only sine
(b) Only cosine
(c) Only tangent
(d) All trigonometric functions

Answer: (d) All trigonometric functions

Solution: In Quadrant I, all six trigonometric functions are positive.

Q37. In the second quadrant, which function is positive?

(a) sin θ
(b) cos θ
(c) tan θ
(d) sec θ

Answer: (a) sin θ

Solution: In Quadrant II, sine and cosecant are positive.

Q38. In the third quadrant, which function is positive?

(a) sin θ
(b) cos θ
(c) tan θ
(d) sec θ

Answer: (c) tan θ

Solution: In Quadrant III, tangent and cotangent are positive.

Q39. In the fourth quadrant, which function is positive?

(a) sin θ
(b) cos θ
(c) tan θ
(d) cosec θ

Answer: (b) cos θ

Solution: In Quadrant IV, cosine and secant are positive.

Q40. If sin θ > 0 and cos θ < 0, then θ lies in:

(a) Quadrant I
(b) Quadrant II
(c) Quadrant III
(d) Quadrant IV

Answer: (b) Quadrant II

Solution: Sine is positive and cosine is negative in Quadrant II.

Q41. If tan θ > 0 and sin θ < 0, then θ lies in:

(a) Quadrant I
(b) Quadrant II
(c) Quadrant III
(d) Quadrant IV

Answer: (c) Quadrant III

Solution: Tangent is positive in Quadrants I and III. Since sine is negative, θ lies in Quadrant III.

Q42. If cos θ > 0 and sin θ < 0, then θ lies in:

(a) Quadrant I
(b) Quadrant II
(c) Quadrant III
(d) Quadrant IV

Answer: (d) Quadrant IV

Solution: Cosine is positive and sine is negative in Quadrant IV.

Q43. The ASTC rule helps determine:

(a) Angle measurement only
(b) Radius of circle only
(c) Signs of trigonometric functions
(d) Arc length only

Answer: (c) Signs of trigonometric functions

Solution: ASTC tells which trigonometric functions are positive in different quadrants.

MCQs on Domain, Range and Periodicity

Q44. The domain of sin x is:

(a) R
(b) R − {0}
(c) [−1,1]
(d) Positive real numbers only

Answer: (a) R

Solution:sin x is defined for all real values of x.

Q45. The range of sin x is:

(a) R
(b) [−1,1]
(c) [0,∞)
(d) R − {0}

Answer: (b) [−1,1]

Solution: The value of sine always lies between −1 and 1.

Q46. The domain of cos x is:

(a) R
(b) [−1,1]
(c) R − {0}
(d) Integers only

Answer: (a) R

Solution:cos x is defined for all real values of x.

Q47. The range of cos x is:

(a) R
(b) [−1,1]
(c) [0,1]
(d) R − {0}

Answer: (b) [−1,1]

Solution: The value of cosine always lies between −1 and 1.

Q48. The period of sin x is:

(a) π/2
(b) π
(c) 2π
(d) 4π

Answer: (c) 2π

Solution:sin(x + 2π) = sin x, so the period is 2π.

Q49. The period of tan x is:

(a) π/2
(b) π
(c) 2π
(d) 4π

Answer: (b) π

Solution:tan(x + π) = tan x, so the period of tangent is π.

Q50. tan x is not defined when:

(a) sin x = 0
(b) cos x = 0
(c) sin x = cos x
(d) x = 0 only

Answer: (b) cos x = 0

Solution: Since tan x = sin x/cos x, it is undefined when cos x = 0.

Q51. The range of sec x is:

(a) [−1,1]
(b) R
(c) (-∞,−1] ∪ [1,∞)
(d) [0,∞)

Answer: (c) (-∞,−1] ∪ [1,∞)

Solution: Since sec x = 1/cos x and cos x ∈ [−1,1], secant values are ≤ −1 or ≥ 1.

Q52. The range of cosec x is:

(a) [−1,1]
(b) R
(c) (-∞,−1] ∪ [1,∞)
(d) [0,1]

Answer: (c) (-∞,−1] ∪ [1,∞)

Solution: Since cosec x = 1/sin x, its values are ≤ −1 or ≥ 1.

MCQs on Basic Trigonometric Identities

Q53. Which identity is correct?

(a) sin²x − cos²x = 1
(b) sin²x + cos²x = 1
(c) tan²x + cot²x = 1
(d) sec²x + cosec²x = 1

Answer: (b) sin²x + cos²x = 1

Solution: This is the fundamental Pythagorean identity.

Q54. 1 + tan²x is equal to:

(a) cosec²x
(b) sec²x
(c) sin²x
(d) cos²x

Answer: (b) sec²x

Solution: The identity is 1 + tan²x = sec²x.

Q55. 1 + cot²x is equal to:

(a) sec²x
(b) cosec²x
(c) tan²x
(d) sin²x

Answer: (b) cosec²x

Solution: The identity is 1 + cot²x = cosec²x.

Q56. sec²x − tan²x is equal to:

(a) 0
(b) 1
(c) sin x
(d) cos x

Answer: (b) 1

Solution: From 1 + tan²x = sec²x, we get sec²x − tan²x = 1.

Q57. cosec²x − cot²x is equal to:

(a) 0
(b) 1
(c) tan x
(d) sec x

Answer: (b) 1

Solution: From 1 + cot²x = cosec²x, we get cosec²x − cot²x = 1.

Q58. tan x is equal to:

(a) cos x/sin x
(b) sin x/cos x
(c) 1/sin x
(d) 1/cos x

Answer: (b) sin x/cos x

Solution: By definition, tan x = sin x/cos x.

Q59. cot x is equal to:

(a) sin x/cos x
(b) cos x/sin x
(c) 1/cos x
(d) 1/sin x

Answer: (b) cos x/sin x

Solution: By definition, cot x = cos x/sin x.

Q60. If sin x = 3/5 and x is acute, then cos x is:

(a) 3/5
(b) 4/5
(c) 5/3
(d) 5/4

Answer: (b) 4/5

Solution:
sin²x + cos²x = 1
(3/5)² + cos²x = 1
9/25 + cos²x = 1
cos²x = 16/25
Since x is acute, cos x = 4/5.

MCQs on Allied Angles

Q61. sin(−x) is equal to:

(a) sin x
(b) −sin x
(c) cos x
(d) −cos x

Answer: (b) −sin x

Solution: Sine is an odd function, so sin(−x) = −sin x.

Q62. cos(−x) is equal to:

(a) cos x
(b) −cos x
(c) sin x
(d) −sin x

Answer: (a) cos x

Solution: Cosine is an even function, so cos(−x) = cos x.

Q63. sin(90° − x) is equal to:

(a) sin x
(b) −sin x
(c) cos x
(d) −cos x

Answer: (c) cos x

Solution: Complementary angle identity: sin(90° − x) = cos x.

Q64. cos(90° − x) is equal to:

(a) sin x
(b) cos x
(c) −sin x
(d) −cos x

Answer: (a) sin x

Solution: Complementary angle identity: cos(90° − x) = sin x.

Q65. sin(180° − x) is equal to:

(a) sin x
(b) −sin x
(c) cos x
(d) −cos x

Answer: (a) sin x

Solution: In Quadrant II, sine is positive, so sin(180° − x) = sin x.

Q66. cos(180° − x) is equal to:

(a) cos x
(b) −cos x
(c) sin x
(d) −sin x

Answer: (b) −cos x

Solution: In Quadrant II, cosine is negative, so cos(180° − x) = −cos x.

MCQs on Compound Angle Formulas

Q67. sin(A+B) is equal to:

(a) sin A cos B + cos A sin B
(b) sin A cos B − cos A sin B
(c) cos A cos B − sin A sin B
(d) cos A cos B + sin A sin B

Answer: (a) sin A cos B + cos A sin B

Solution: This is the standard formula for sine of the sum of two angles.

Q68. cos(A+B) is equal to:

(a) cos A cos B + sin A sin B
(b) cos A cos B − sin A sin B
(c) sin A cos B + cos A sin B
(d) sin A sin B − cos A cos B

Answer: (b) cos A cos B − sin A sin B

Solution: This is the standard formula for cosine of the sum of two angles.

Q69. cos(A−B) is equal to:

(a) cos A cos B + sin A sin B
(b) cos A cos B − sin A sin B
(c) sin A cos B + cos A sin B
(d) sin A cos B − cos A sin B

Answer: (a) cos A cos B + sin A sin B

Solution: This is the standard formula for cosine of the difference of two angles.

Q70. tan(A+B) is equal to:

(a) (tan A − tan B)/(1 + tan A tan B)
(b) (tan A + tan B)/(1 − tan A tan B)
(c) (tan A + tan B)/(1 + tan A tan B)
(d) (tan A − tan B)/(1 − tan A tan B)

Answer: (b) (tan A + tan B)/(1 − tan A tan B)

Solution: This is the standard formula for tangent of sum of two angles.

Q71. The value of sin 75° is:

(a) (√3 + 1)/(2√2)
(b) (√3 − 1)/(2√2)
(c) 1/2
(d) √3/2

Answer: (a) (√3 + 1)/(2√2)

Solution:
sin 75° = sin(45° + 30°)
= sin45°cos30° + cos45°sin30°
= (1/√2)(√3/2) + (1/√2)(1/2)
= (√3 + 1)/(2√2).

Q72. The value of cos 75° is:

(a) (√3 + 1)/(2√2)
(b) (√3 − 1)/(2√2)
(c) √3/2
(d) 1/2

Answer: (b) (√3 − 1)/(2√2)

Solution:
cos 75° = cos(45° + 30°)
= cos45°cos30° − sin45°sin30°
= (1/√2)(√3/2) − (1/√2)(1/2)
= (√3 − 1)/(2√2).

Q73. tan 75° is equal to:

(a) 2 + √3
(b) 2 − √3
(c) √3 − 1
(d) √3 + 1

Answer: (a) 2 + √3

Solution:
tan 75° = tan(45° + 30°)
= (1 + 1/√3)/(1 − 1/√3)
= 2 + √3.

MCQs on Trigonometric Equations

Q74. The general solution of sin x = 0 is:

(a) x = nπ, n ∈ Z
(b) x = 2nπ, n ∈ Z
(c) x = (2n+1)π/2, n ∈ Z
(d) x = π/4

Answer: (a) x = nπ, n ∈ Z

Solution: Sine becomes zero at integral multiples of π.

Q75. The general solution of cos x = 0 is:

(a) x = nπ
(b) x = 2nπ
(c) x = (2n+1)π/2
(d) x = π/6

Answer: (c) x = (2n+1)π/2

Solution: Cosine becomes zero at odd multiples of π/2.

Q76. The general solution of tan x = 0 is:

(a) x = nπ, n ∈ Z
(b) x = (2n+1)π/2
(c) x = π/4
(d) x = 2nπ + π/6

Answer: (a) x = nπ, n ∈ Z

Solution: Tangent becomes zero when sine is zero and cosine is non-zero.

Q77. The number of solutions of sin x = 1 in [0, 2π] is:

(a) 0
(b) 1
(c) 2
(d) 3

Answer: (b) 1

Solution:sin x = 1 only at x = π/2 in [0, 2π].

Q78. The number of solutions of cos x = 1 in [0, 2π] is:

(a) 1
(b) 2
(c) 3
(d) 4

Answer: (b) 2

Solution:cos x = 1 at x = 0 and x = 2π in [0, 2π].

Q79. The number of solutions of tan x = 1 in [0, 2π) is:

(a) 1
(b) 2
(c) 3
(d) 4

Answer: (b) 2

Solution:tan x = 1 at x = π/4 and x = 5π/4 in [0, 2π).

Q80. The principal solution of sin x = 1/2 in [0, 2π] is:

(a) π/6, 5π/6
(b) π/3, 2π/3
(c) π/4, 3π/4
(d) 0, π

Answer: (a) π/6, 5π/6

Solution: Sine is positive in Quadrants I and II. Therefore, x = π/6 and x = 5π/6.

JEE-Level Trigonometric Functions MCQs

Q81. If sin x + cos x = 1, then sin x cos x is:

(a) 0
(b) 1
(c) 1/2
(d) −1/2

Answer: (a) 0

Solution:
Square both sides:
(sin x + cos x)² = 1
sin²x + cos²x + 2sin x cos x = 1
1 + 2sin x cos x = 1
sin x cos x = 0.

Q82. If tan x + cot x = 2, then the value of tan²x + cot²x is:

(a) 0
(b) 1
(c) 2
(d) 4

Answer: (c) 2

Solution:
Let a = tan x and b = cot x. Since tan x cot x = 1,
(a+b)² = a² + b² + 2ab
2² = a² + b² + 2
a² + b² = 2.

Q83. If sin θ = cos θ, then tan θ is:

(a) 0
(b) 1
(c) √3
(d) Not defined

Answer: (b) 1

Solution:
If sin θ = cos θ, then dividing by cos θ,
tan θ = 1.

Q84. If sin θ = 5/13 and θ is in Quadrant II, then cos θ is:

(a) 12/13
(b) −12/13
(c) 5/12
(d) −5/12

Answer: (b) −12/13

Solution:
sin²θ + cos²θ = 1
25/169 + cos²θ = 1
cos²θ = 144/169
cos θ = ±12/13.
In Quadrant II, cosine is negative, so cos θ = −12/13.

Q85. If cos θ = −3/5 and θ lies in Quadrant III, then sin θ is:

(a) 4/5
(b) −4/5
(c) 3/4
(d) −3/4

Answer: (b) −4/5

Solution:
sin²θ + cos²θ = 1
sin²θ + 9/25 = 1
sin²θ = 16/25
In Quadrant III, sine is negative, so sin θ = −4/5.

Trigonometric Functions MCQ Answer Key

Common Mistakes in Trigonometric Functions MCQs

1. Confusing degrees and radians

Always check whether the question gives the angle in degrees or radians. For example, π/2 means 90°, not 180°.

2. Using degree formulas when the angle is in radians

If the angle is in radians, use radian-based formulas. For arc length, l = rθ works only when θ is in radians.

3. Forgetting quadrant signs

A value like sin θ = 5/13 does not fully determine cos θ unless the quadrant is given.

4. Treating tan x as defined everywhere

tan x is undefined when cos x = 0, such as at π/2, 3π/2, etc.

5. Forgetting reciprocal identities

Remember:

sec x = 1/cos x
cosec x = 1/sin x
cot x = 1/tan x

6. Assuming sin(A+B) = sin A + sin B

This is incorrect. The correct formula is:

sin(A+B) = sin A cos B + cos A sin B

7. Forgetting periodicity

sin x and cos x have period 2π, while tan x and cot x have period π/.