250+ TOP MCQs on Trigonometric Functions & Answers | Class 11 Maths

Mathematics Multiple Choice Questions on “Trigonometric Functions – 1”.

1. If sin x=0 then x = ________
a) nπ
b) (2n+1) π/2
c) (n+1) π
d) nπ/2
Answer: a
Clarification: When know, sin x =0 whenever x is 0, π, 2π, 3π,….. i.e. all integral multiples of π so, x=nπ when sin x=0.

2. If cos x=0 then x = ________
a) nπ
b) (2n+1) π/2
c) (n+1) π
d) nπ/2
Answer: b
Clarification: When know, cos x =0 whenever x is π/2, 3π/2, 5π/2, ………… i.e. all odd integral multiples of π/2
so, x=(2n+1) π/2 when cos x=0.

3. If tan x = 0 then x = _________
a) nπ
b) (2n+1) π/2
c) (n+1) π
d) nπ/2
Answer: a
Clarification: We know, tan x = sin x / cos x. So, tan x will be zero wherever sin x is zero except the points where cos x is also zero. We know there is no point where sin x as well as cos x both are zero. So, tan x = 0 => x=nπ.

4. 1-sin245° = ___________
a) 1/2
b) 1
c) 0
d) √3 /2
Answer: a
Clarification: We know, sin²45° + cos²45°=1
So, 1- sin²45° = cos²45° = (1/√2)² = 1/2.

5. 1-cos²x=_________
a) sin x
b) cos x
c) sin 2x
d) sin²x
Answer: d
Clarification: We know, sin²x+ cos²x=1
So, 1-cos²x=sin²x.

6. 1-sec²x=_________
a) cot²x
b) tan²x
c) -tan²x
d) -cot²x
Answer: c
Clarification: We know, sec²x – tan²x=1
So, 1-sec²x=-tan²x.

7. 1+ tan²x=_______________
a) sec²x
b) -sec²x
c) cosec²x
d) -cosec²x
Answer: a
Clarification: We know, sec²x – tan²x=1
So, 1+ tan²x=sec²x.

8. cot²x – cosec²x = __________
a) 1
b) -1
c) sin²x
d) cos²x
Answer: b
Clarification: We know, cosec²x – cot²x = 1
So, cot²x – cosec²x = -1.

9. cosec²x – 1 = ______________
a) cot²x
b) -cot²x
c) tan²x
d) -tan²x
Answer: a
Clarification: We know, cosec²x – cot²x = 1
So, cosec²x – 1 = cot²x.

10. tan x is not defined for_______
a) 0
b) nπ/2
c) (2n+1) π/2
d) nπ
Answer: c
Clarification: We know, tan x is not defined when cos x = 0.
cos x = 0 whenever x is π/2, 3π/2, 5π/2, ………… i.e. all odd integral multiples of π/2
so, x=(2n+1) π/2.

11. sin (-45°) = ______________
a) 1
b) -1
c) 1/√2
d) -1/√2
Answer: d
Clarification: We know, sin(-x) = sin x
So, sin (-45°) = -sin 45° = -1/√2.

12. cos (-60°) = ________________
a) -√3/2
b) 1/2
c) √3/2
d) -1/2
Answer: b
Clarification: We know, cos (-x) = cos x
So, cos(-60°) = cos 60°=1/2.