NCERT Class 10 Maths — Chapter 8

Exercise 8.2: Trigonometric Ratios of Standard Angles

Evaluate expressions using the exact values of sin, cos, and tan for 0°, 30°, 45°, 60°, and 90°. Memorise the table — it's used everywhere.

standard angles30° 45° 60° valuestrigonometric table
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Extra Practice Questions

These questions cover the same concepts as Exercise 8.2. Try solving them to build confidence before or after the textbook exercise.

1

If A and B are acute angles such that sin A = 1/2 and cos B = 1/2, what is the value of A + B?

A.30°
B.60°
C.90°
D.120°
2

If sin θ + cos θ = √2, then what is the value of sin θ × cos θ?

A.0
B.1/2
C.1
D.√2
3

A pole stands vertically on the ground. When the angle of elevation of the sun is 30°, the length of the shadow is 'x' meters. When the angle of elevation becomes 60°, the length of the shadow is 'y' meters. Which of the following statements correctly relates 'x' and 'y'?

A.A) x = y
B.B) x > y
C.C) x < y
D.D) x = 2y
4

A ladder is leaning against a wall, making an angle of 60° with the ground. If the foot of the ladder is 2 meters away from the wall, what is the length of the ladder?

A.2 m
B.4 m
C.2√3 m
D.√3 m
5

If A and B are acute angles such that sin A = cos B, then which of the following statements must be true?

A.A) A = B
B.B) A + B = 90°
C.C) A - B = 90°
D.D) A = 2B
6

Which of the following statements is INCORRECT?

A.sin 0° = 0
B.cos 90° = 0
C.tan 45° = 1
D.sec 0° = 0
7

Which of the following statements is NOT possible for an acute angle A?

A.sin A = (p² + 1) / (p² + 2) for some real p
B.sec A = 1/2
C.tan A = 20
D.cos A = (q² - 1) / (q² + 1) for some real q where q ≠ 0
8

If cosec θ - cot θ = 1/2, then cosec θ + cot θ = ______.

A.1/2
B.1
C.2
D.4
9

If sec θ + tan θ = p, what is the value of sec θ - tan θ?

A.p
B.1/p
C.p²
D.1 - p
10

Ravi claims that for an acute angle θ, sin θ can be 2.5. What is the mistake in Ravi's statement?

A.sin θ must be a value between 0 and 1 (inclusive).
B.sin θ must be a value greater than or equal to 1.
C.sin θ must be a value less than 0.
D.There is no mistake; sin θ can be any real value.
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Common Mistakes to Avoid

  • ✗Mixing up sin 30° (= ½) and cos 30° (= √3/2)
  • ✗Forgetting that tan 90° is undefined
  • ✗Not simplifying expressions fully

Other Exercises in Chapter 8

Exercise 8.1
Trigonometric Ratios
Exercise 8.2
Trigonometric Ratios of Standard Angles
Exercise 8.3
Complementary Angles
Exercise 8.4
Trigonometric Identities

Frequently Asked Questions

What are the standard angle values?

sin 30° = ½, cos 30° = √3/2, tan 30° = 1/√3. sin 45° = cos 45° = 1/√2. sin 60° = √3/2, cos 60° = ½, tan 60° = √3.

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