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Greatest or least value of an expression in sin t or sin^2 t using 0 <= sin t <= 1

This type of question, asked 5 times: CDS 2 2020, CDS 1 2021, CDS 1 2023, CDS 1 2024, CDS 2 2026. All 6 questions below, oldest first.

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  1. Question 1

    CDS 2 2020

    56
    What is the least value of 9sin⁡2θ+16cos⁡2θ9 \sin^2 \theta + 16 \cos^2 \theta ?

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  2. Question 2

    CDS 2 2020

    54
    What is the maximum value of 3sin⁡θ−43 \sin \theta - 4 ?

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  3. Question 3

    CDS 1 2021

    46
    What is the least value of 3sin⁡2θ+4cos⁡2θ3\sin^2 \theta + 4\cos^2 \theta ?

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  4. Question 4

    CDS 1 2023

    49
    What is the minimum value of 6−4sin⁡θ6 - 4\sin\theta, 0≤θ≤π20 \le \theta \le \frac{\pi}{2} ?

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  5. Question 5

    CDS 1 2024

    12
    What is the difference between the greatest value and the least value of cos⁡2θ+3sin⁡2θ+2\cos^2 \theta + 3 \sin^2 \theta + 2 ?

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  6. Question 6

    CDS 2 2026

    47
    What is the ratio of the greatest value of sin⁡2x+2\sin^2 x + 2 (where 0≤x≤π20 \le x \le \frac{\pi}{2}) to its least value ?

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