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Class 10 Maths Chapter 8: Introduction to Trigonometry MCQs with answers

10 multiple-choice questions on Introduction to Trigonometry, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
In ΔABC, right-angled at B, AB = 5 cm, BC = 12 cm and AC = 13 cm. The value of sin A is
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Answer: (a) 1213

The side opposite A is BC = 12 cm and the hypotenuse is AC = 13 cm, so sin A = 12/13.

Question 2
In ΔPQR, right-angled at Q, PQ = 8 cm, QR = 15 cm and PR = 17 cm. The value of cos R is
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Answer: (b) 1517

For angle R the adjacent side is QR = 15 cm and the hypotenuse is PR = 17 cm, so cos R = 15/17. (8/17 is cos P.)

Question 3
In ΔXYZ, right-angled at Y, XY = 7 cm, YZ = 24 cm and XZ = 25 cm. The value of tan Z is
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Answer: (c) 724

For angle Z the opposite side is XY = 7 cm and the adjacent side is YZ = 24 cm, so tan Z = 7/24.

Question 4
If sin A = 23, then cosec A is
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Answer: (d) 32

cosec A is the reciprocal of sin A, so cosec A = 1 ÷ (2/3) = 3/2.

Question 5
The value of tan 45° + sin 45° cos 45° is
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Answer: (a) 32

tan 45° = 1 and sin 45° cos 45° = (1/√2)(1/√2) = 1/2, so the sum is 3/2.

Question 6
The value of 2 sin 30° + √3 cos 30° is
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Answer: (b) 52

2 sin 30° = 2 × 1/2 = 1 and √3 cos 30° = √3 × √3/2 = 3/2, so the value is 1 + 3/2 = 5/2.

Question 7
The value of tan 60°tan 30° is
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Answer: (c) 3

tan 60° = √3 and tan 30° = 1/√3, so the quotient is √3 × √3 = 3.

Question 8
In a right triangle one acute angle is 45° and the hypotenuse is 10√2 cm. The length of each of the other two sides is
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Answer: (d) 10 cm

The other acute angle is also 45°, so the legs are equal. Each leg = hypotenuse × sin 45° = 10√2 × 1/√2 = 10 cm.

Question 9
The expression sin²A stands for
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Answer: (a) (sin A)²

sin²A is the notation for (sin A)², the square of the sine of A. It is not the sine of A², and 'sin' on its own is not a number that can multiply anything.

Question 10
The value of cos 0° + sin 90° + sin 0° is
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Answer: (c) 2

cos 0° = 1, sin 90° = 1 and sin 0° = 0, so the sum is 2.

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