Chapter Exam

Chapter 8: Introduction to Trigonometry — Online MCQ Test

Q: In a right-angled triangle, sin A is equal to:

Answer: A. Opposite side/Hypotenuse — By definition, sin A = perpendicular or opposite side divided by hypotenuse.

Q: The value of tan A in terms of sin A and cos A is:

Answer: B. sin A/cos A — The identity tan A = sin A/cos A is a basic trigonometric relation.

Q: In a right triangle, for an acute angle A, the side opposite A is 3 cm and the hypotenuse is 5 cm. What is sin A?

Answer: A. 3/5 — sin A = opposite side/hypotenuse = 3/5.

Q: If sin A + cos A = √2 for an acute angle A, then tan A + cot A is:

Answer: B. 2 — Squaring sin A + cos A = √2 gives 1 + 2 sin A cos A = 2, so sin A cos A = 1/2. Thus tan A + cot A = 1/(sin A cos A) = 2.

Q: If tan θ + sec θ = p, then (1 - sin θ)/(1 + sin θ) is equal to:

Answer: B. 1/p² — Since tan θ + sec θ = (1 + sin θ)/cos θ = p and sec θ - tan θ = 1/p, the ratio (1 - sin θ)/(1 + sin θ) = 1/p².

MATHS · CLASS 10 · Andhra State Board

Practice Chapter 8: Introduction to Trigonometry with a free chapter-wise online MCQ test for Andhra State Board CLASS 10 MATHS. This chapter covers: Trigonometric ratios Sine Cosine Tangent Cosecant Secant Cotangent Standard angles Trigonometric identities Complementary angles. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 8: Introduction to Trigonometry — Important Questions & Answers (FAQ)

Frequently asked questions from Andhra State Board CLASS 10 MATHS — Chapter 8: Introduction to Trigonometry, with answers and explanations. These are sample questions; the exam has its own separate question set.

In a right-angled triangle, sin A is equal to:

A. Opposite side/Hypotenuse ✓
B. Adjacent side/Hypotenuse
C. Opposite side/Adjacent side
D. Hypotenuse/Opposite side

Answer: A. Opposite side/Hypotenuse
By definition, sin A = perpendicular or opposite side divided by hypotenuse.

The value of tan A in terms of sin A and cos A is:

A. cos A/sin A
B. sin A/cos A ✓
C. 1/(sin A cos A)
D. sin A + cos A

Answer: B. sin A/cos A
The identity tan A = sin A/cos A is a basic trigonometric relation.

In a right triangle, for an acute angle A, the side opposite A is 3 cm and the hypotenuse is 5 cm. What is sin A?

A. 3/5 ✓
B. 4/5
C. 3/4
D. 5/3

Answer: A. 3/5
sin A = opposite side/hypotenuse = 3/5.

If sin A + cos A = √2 for an acute angle A, then tan A + cot A is:

A. 1
B. 2 ✓
C. √2
D. 4

Answer: B. 2
Squaring sin A + cos A = √2 gives 1 + 2 sin A cos A = 2, so sin A cos A = 1/2. Thus tan A + cot A = 1/(sin A cos A) = 2.

If tan θ + sec θ = p, then (1 - sin θ)/(1 + sin θ) is equal to:

A. p²
B. 1/p² ✓
C. p
D. 1/p

Answer: B. 1/p²
Since tan θ + sec θ = (1 + sin θ)/cos θ = p and sec θ - tan θ = 1/p, the ratio (1 - sin θ)/(1 + sin θ) = 1/p².

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