Class 10 Maths – Introduction to Trigonometry MCQ

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1. If sin θ = 3/5 and θ is an acute angle, then cos θ is:

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

Answer:

a) 4/5

Explanation:

Using the Pythagorean identity, cos² θ = 1 – sin² θ. So, cos θ = √(1 – (3/5)²) = 4/5.

2. The value of tan 45° is:

a) 0
b) 1
c) √2
d) √3

Answer:

b) 1

Explanation:

tan 45° = sin 45°/cos 45° = 1/√2 ÷ 1/√2 = 1.

3. If cos A = 1/√2, then the value of A is:

a) 0°
b) 30°
c) 45°
d) 60°

Answer:

c) 45°

Explanation:

cos 45° = 1/√2.

4. The reciprocal of cosec θ is:

a) sin θ
b) cos θ
c) sec θ
d) tan θ

Answer:

a) sin θ

Explanation:

cosec θ is the reciprocal of sin θ.

5. The value of sin²θ + cos²θ is always:

a) 0
b) 1
c) θ
d) 2

Answer:

b) 1

Explanation:

This is the fundamental Pythagorean identity in trigonometry.

6. The trigonometric ratio which is independent of θ in the first quadrant is:

a) sin θ
b) cos θ
c) sec θ
d) tan θ

Answer:

c) sec θ

Explanation:

In the first quadrant, all trigonometric ratios are positive.

7. If tan θ = √3, then the value of sin θ is:

a) 1/2
b) √3/2
c) 1/√2
d) 1/√3

Answer:

b) √3/2

Explanation:

For tan θ = √3, θ = 60°. So, sin 60° = √3/2.

8. The value of cos 90° is:

a) 0
b) 1
c) -1
d) √2

Answer:

a) 0

Explanation:

cos 90° = 0 as the cosine function represents the x-coordinate on the unit circle.

9. If sin θ = x and cos θ = y, then (x² + y²) equals:

a) 1
b) 0
c) x
d) y

Answer:

a) 1

Explanation:

Given, sin²θ + cos²θ = 1.

10. The general solution for the equation sin x = 0 is:

a) nπ, where n is an integer
b) (2n+1)π/2, where n is an integer
c) nπ/2, where n is an integer
d) π/n, where n is an integer

Answer:

a) nπ, where n is an integer

Explanation:

sin function is zero at integral multiples of π.

11. If sec A = 13/12, then tan A is:

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

Answer:

b) 5/13

Explanation:

tan A = √(sec²A – 1) = 5/13.

12. For which of the following angles, sin and cos have the same value?

a) 30°
b) 45°
c) 60°
d) 90°

Answer:

b) 45°

Explanation:

sin 45° = cos 45° = 1/√2.

13. The period of the function sin(x) is:

a) π
b) 2π
c) π/2
d) 4π

Answer:

b) 2π

Explanation:

The function sin(x) repeats after an interval of 2π.

14. Which trigonometric ratio is always positive?

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

Answer:

d) sec

Explanation:

sec is positive in the first and fourth quadrants.

15. The maximum value of sin x is:

a) 0
b) 1
c) 2
d) x

Answer:

b) 1

Explanation:

The sine function oscillates between -1 and 1.

16. The value of tan(A + B) in terms of tan A and tan B is:

a) 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

Answer:

b) (tan A + tan B)/(1 – tan A tan B)

Explanation:

This is the compound angle formula for tan(A + B).

17. If sin θ = a/c, then csc θ is:

a) a/c
b) c/a
c) a/b
d) c/b

Answer:

b) c/a

Explanation:

csc θ is the reciprocal of sin θ.

18. The range of the sine function is:

a) [0,1]
b) [-1,1]
c) [0,∞)
d) (-∞,∞)

Answer:

b) [-1,1]

Explanation:

The sine function varies between -1 and 1.

19. If cos θ = 0, then θ is:

a) 0°
b) 90°
c) 45°
d) 60°

Answer:

b) 90°

Explanation:

cos 90° = 0.

20. The trigonometric ratio that represents the length of the side opposite to the angle to the hypotenuse is:

a) sin
b) cos
c) tan
d) cot

Answer:

a) sin

Explanation:

Sin θ = Opposite side/Hypotenuse.

Related MCQ (Multiple Choice Questions) :

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