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Question (11)

QN0036831

11. If sin A = 3/5, where A is acute, then cos A is:

(A) 4/5
(B) 3/4
(C) 5/4
(D) 2/5

Correct Answer: A

Explanation:

cos²A = 1 − sin²A = 1 − 9/25 = 16/25. Hence cos A = 4/5.

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Question (12)

QN0036832

12. If cos A = 5/13, then sin A is:

(A) 12/13
(B) 5/12
(C) 8/13
(D) 13/12

Correct Answer: A

Explanation:

sin²A = 1 − 25/169 = 144/169. Therefore, sin A = 12/13.

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Question (13)

QN0036833

13. If tan A = 5/12, then sec A is:

(A) 5/13
(B) 12/13
(C) 13/12
(D) 13/5

Correct Answer: C

Explanation:

The sides are in the ratio 5:12:13. Thus sec A = 13/12.

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Question (14)

QN0036834

14. If cot A = 7/24, then cosec A is:

(A) 24/25
(B) 25/24
(C) 7/25
(D) 25/7

Correct Answer: B

Explanation:

Adjacent:opposite = 7:24, so the hypotenuse is 25. Hence cosec A = 25/24.

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Question (15)

QN0036835

15. If sec A = 17/8, then tan A is:

(A) 8/15
(B) 15/8
(C) 17/15
(D) 15/17

Correct Answer: B

Explanation:

tan²A = sec²A − 1 = 289/64 − 1 = 225/64. Thus tan A = 15/8.

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Question (16)

QN0036836

16. If sin A = 8/17, then cot A equals:

(A) 8/15
(B) 15/8
(C) 17/8
(D) 15/17

Correct Answer: B

Explanation:

From the 8-15-17 triangle, opposite = 8 and adjacent = 15. Therefore cot A = 15/8.

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Question (17)

QN0036837

17. If tan A = 3/4, then sin A + cos A is:

(A) 7/5
(B) 1
(C) 1/5
(D) 6/5

Correct Answer: A

Explanation:

From the 3-4-5 triangle, sin A = 3/5 and cos A = 4/5. Hence sin A + cos A = 7/5.

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Question (18)

QN0036838

18. If sin A = 3/5, then sin A cos A is:

(A) 3/25
(B) 4/25
(C) 12/25
(D) 7/25

Correct Answer: C

Explanation:

cos A = 4/5. Therefore, sin A cos A = (3/5)(4/5) = 12/25.

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Question (19)

QN0036839

19. If cos A = 12/13, then tan A is:

(A) 5/12
(B) 12/5
(C) 5/13
(D) 13/12

Correct Answer: A

Explanation:

The third side is 5, so tan A = opposite/adjacent = 5/12.

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Question (20)

QN0036840

20. If sin A = 5/13, then sec A − tan A equals:

(A) 1/3
(B) 2/3
(C) 3/4
(D) 4/3

Correct Answer: B

Explanation:

cos A = 12/13, so sec A = 13/12 and tan A = 5/12. Thus sec A − tan A = 8/12 = 2/3.

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Question (11)

11. If sin A = 3/5, where A is acute, then cos A is:

Explanation:

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Question (12)

12. If cos A = 5/13, then sin A is:

Explanation:

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Question (13)

13. If tan A = 5/12, then sec A is:

Explanation:

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Question (14)

14. If cot A = 7/24, then cosec A is:

Explanation:

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Question (15)

15. If sec A = 17/8, then tan A is:

Explanation:

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Question (16)

16. If sin A = 8/17, then cot A equals:

Explanation:

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Question (17)

17. If tan A = 3/4, then sin A + cos A is:

Explanation:

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Question (18)

18. If sin A = 3/5, then sin A cos A is:

Explanation:

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Question (19)

19. If cos A = 12/13, then tan A is:

Explanation:

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Question (20)

20. If sin A = 5/13, then sec A − tan A equals:

Explanation:

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