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Complementary angles: ratio of one angle given, find a ratio of the other

This type of question, asked 6 times: 27 Jul 2023 S1, 11 Sep 2024 S2, 12 Sep 2025 S2, 21 Sep 2025 S1, 24 Sep 2025 S1, 26 Sep 2025 S3. All 8 questions below, oldest first.

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  1. Question 1

    27 Jul 2023 S1

    64
    Given θ1+θ2=π2\theta_1 + \theta_2 = \frac{\pi}{2} and sin⁡θ1=12\sin \theta_1 = \frac{1}{2}, find the value of θ2\theta_2.

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  2. Question 2

    27 Jul 2023 S1

    59
    If A+B=90∘A + B = 90^\circ and sin⁡A=35\sin A = \frac{3}{5}, then the value of tanB is ________.

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  3. Question 3

    11 Sep 2024 S2

    59
    In a triangle ΔABC\Delta ABC, the ∠ABC=90∘\angle ABC = 90^\circ. If sin⁡(A)=12\sin(A) = \frac{1}{2}, then cos⁡(C)\cos(C) is equal to:

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  4. Question 4

    12 Sep 2025 S2

    70
    If tan⁡(90∘−A)=3\tan(90^\circ - A) = \sqrt{3}, what is sin A?

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  5. Question 5

    21 Sep 2025 S1

    71
    If sin⁡A=45\sin A = \frac{4}{5} and A is acute, find cot⁡(90∘−A)\cot(90^\circ - A).

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  6. Question 6

    24 Sep 2025 S1

    72
    If A+B=90∘A + B = 90^\circ and tan⁡A=2\tan A = 2, determine the value of tan⁡A×tan⁡B\tan A \times \tan B.

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  7. Question 7

    26 Sep 2025 S3

    65
    In Δ\DeltaABC, right-angled at C, if sin⁡A=513\sin A = \frac{5}{13}, then cos B = ?

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  8. Question 8

    26 Sep 2025 S3

    67
    If A + B = 90∘90^\circ, and sin⁡A=513\sin A = \frac{5}{13}, then what is cos B?

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