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One ratio given with its quadrant: find another ratio with the right sign

This type of question, asked 7 times: 17 Jul 2023 S3, 18 Jul 2023 S2, 24 Jul 2023 S2, 17 Sep 2025 S3, 22 Sep 2025 S1, 23 Sep 2025 S2, 23 Sep 2025 S3. All 7 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    17 Jul 2023 S3

    68
    If cos⁡x=−12\cos x = -\frac{1}{2}, x lies in third quadrant, then tan⁡x=\tan x = ?

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  2. Question 2

    18 Jul 2023 S2

    71
    If sin⁡A=−35\sin A = -\frac{3}{5}, AA lies in III quadrant, the value of sec⁡A\sec A is:

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  3. Question 3

    24 Jul 2023 S2

    62
    If tan⁡x=−125\tan x = -\frac{12}{5}, where x lies in the second quadrant, what is the value of sin⁡x−cot⁡x\sin x - \cot x?

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  4. Question 4

    17 Sep 2025 S3

    64
    If sin⁡A=35\sin A = \frac{3}{5} and A lies in the second quadrant, find the value of (sin⁡A+cos⁡A)2(\sin A + \cos A)^2.

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  5. Question 5

    22 Sep 2025 S1

    67
    If sin⁡A=513\sin A = \frac{5}{13} and A lies in 2nd quadrant, then find the value of sin⁡A×sec⁡A\sin A \times \sec A.

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  6. Question 6

    23 Sep 2025 S2

    70
    If sin⁡A=45\sin A = \frac{4}{5} and A lies in 2nd quadrant, find the value of (1+tan⁡A)(1−tan⁡A)(1 + \tan A)(1 - \tan A).

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  7. Question 7

    23 Sep 2025 S3

    68
    If sin⁡A=35\sin A = \frac{3}{5} and A lies in the 2nd quadrant, what is the value of tan⁡A\tan A?

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