PYQ Vault

One ratio given as a number: find one other ratio (Pythagorean triple)

This type of question, asked 15 times: 21 Jul 2023 S4, 25 Jul 2023 S1, 26 Jul 2023 S2, 27 Jul 2023 S3, 9 Sep 2024 S2, 17 Sep 2024 S3, 12 Sep 2025 S2, 17 Sep 2025 S1, 20 Sep 2025 S1, 21 Sep 2025 S1, 22 Sep 2025 S3, 23 Sep 2025 S1, 24 Sep 2025 S1, 24 Sep 2025 S2, 26 Sep 2025 S3. All 15 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    21 Jul 2023 S4

    51
    If 8 cot A = 7, find sin A.

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  2. Question 2

    25 Jul 2023 S1

    62
    If tan⁡α=6\tan\alpha = 6, then sec⁡α\sec\alpha equals to:

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  3. Question 3

    26 Jul 2023 S2

    68
    In a right triangle for an acute angle x, if sin⁡x=37\sin x = \frac{3}{7}, then find the value of cos⁡x\cos x.

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  4. Question 4

    27 Jul 2023 S3

    73
    If 7 cot P = 24, then find sin P.

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  5. Question 5

    9 Sep 2024 S2

    51
    What is the value of sec⁡(t)\sec(t), if tan⁡(t)=13\tan(t) = \frac{1}{3}?

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  6. Question 6

    17 Sep 2024 S3

    51
    If tan⁡(A)=35\tan(A) = \frac{3}{5}, then cos⁡(A)\cos(A) is equal to:

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  7. Question 7

    12 Sep 2025 S2

    75
    If sec⁡A=135\sec A = \frac{13}{5} and A is acute, find sin⁡A\sin A.

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  8. Question 8

    17 Sep 2025 S1

    64
    If sin⁡θ=1213\sin\theta = \frac{12}{13}, and θ∈(0,π/2)\theta \in (0, \pi/2), then what is the value of tan⁡θ\tan\theta?

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  9. Question 9

    20 Sep 2025 S1

    67
    If cot⁡A=724\cot A = \frac{7}{24}, then what is cosec⁡A\operatorname{cosec} A?

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  10. Question 10

    21 Sep 2025 S1

    69
    If sin⁡A=0.6\sin A = 0.6 and cos⁡A=0.8\cos A = 0.8, what is tan⁡A\tan A?

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  11. Question 11

    22 Sep 2025 S3

    75
    If sin⁡x=110\sin x = \frac{1}{\sqrt{10}}, then find sec⁡x\sec x in simplest form.

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  12. Question 12

    23 Sep 2025 S1

    66
    If sin⁡A=0.6\sin A = 0.6, what is the value of tan⁡A\tan A ?

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  13. Question 13

    24 Sep 2025 S1

    70
    If sec⁡A=1312\sec A = \frac{13}{12} and A is acute, find sin⁡A\sin A.

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  14. Question 14

    24 Sep 2025 S2

    67
    If tan⁡A=34\tan A = \frac{3}{4}, then what is the value of sin⁡A\sin A?

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  15. Question 15

    26 Sep 2025 S3

    74
    If tan A = 3/4, find sin A.

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