Signs, ranges, periodicity and graphs of trigonometric functions

Sub-topic 1 2025 · National One-Eighth Free

$\cos(a-b)$ given $\sin a=\dfrac{3}{5}$, $\cos b=-\dfrac{1}{2}$, both $a$, $b$ obtuse

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Sub-topic 2 2025 · National One-Eighth Premium

Riddle: identifying a trig function from period, amplitude and zeros

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Sub-topic 3 2024 · National One-Eighth Premium

Greatest value of $6\cos\theta+8\sin\theta$ is $10$ (true/false)

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Sub-topic 4 2024 · National One-Eighth Premium

Maximum values of trig functions within restricted intervals (true/false)

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Sub-topic 5 2024 · National Preliminary Premium

Sign properties of sine, cosine and tangent in each quadrant (true/false)

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Sub-topic 6 2024 · National Preliminary Premium

Riddle: identifying a trig function from its period and maximum

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Sub-topic 7 2024 · National Preliminary Premium

Least and greatest value of $\dfrac{15}{2\sin x+5}$

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Sub-topic 8 2024 · National Semifinal Premium

Greatest and least value of $|6\sin x-5|$

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Sub-topic 9 2023 · National One-Eighth Premium

Solving $\csc x=\dfrac{2}{\sqrt3}$ for $0\lt x\lt2\pi$

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Sub-topic 10 2021 · National Preliminary Premium

Finding the odd one out among $\cos330^\circ$, $\cos30^\circ$, $\cos150^\circ$, $\dfrac{\sqrt3}{2}$

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Sub-topic 11 2026 · National Preliminary Premium

Increasing/decreasing behaviour of sin, cos and tan on $\pi\lt\theta\lt\dfrac{3\pi}{2}$ (true/false)

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Sub-topic 12 2024 · National One-Eighth Premium

Greatest and least value of $|3\cos x-2|$

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Sub-topic 13 2024 · National One-Eighth Premium

Greatest value of a linear combination of sine and cosine (true/false)

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Sub-topic 14 2017 · National Quarterfinal Premium

Range of $y=5-7\sin x$

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Sub-topic 15 2023 · National Preliminary Premium

Range of $y=5\sin x+7$

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Sub-topic 16 2023 · National Final Premium

Least and greatest value of $\dfrac{50}{8\cos x+6\sin x+15}$

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Sub-topic 17 2026 · National Preliminary Premium

Riddle: identifying a sine function from its period, zero and maximum

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Sub-topic 18 2025 · National One-Eighth Premium

Riddle: identifying a sine function from its period, zero and maximum

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Sub-topic 19 2023 · National Preliminary Premium

Monotonicity of $\tan x$, $\sin x$ and $\cos x$ on $0\lt x\lt\pi$ (true/false)

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Sub-topic 20 2013 · National Quarterfinal Premium

Period of $\sin(kx)$, $\cos(kx)$ and $\tan(kx)$

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Sub-topic 21 2013 · National Quarterfinal Premium

$y=\sin x$ is increasing between $0^\circ$ and $90^\circ$ (true/false)

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Sub-topic 22 2013 · National Quarterfinal Premium

$y=\cos x$ is increasing between $90^\circ$ and $180^\circ$ (true/false)

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Sub-topic 23 2013 · National Quarterfinal Premium

$y=\tan x$ is increasing between $0^\circ$ and $90^\circ$ (true/false)

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Sub-topic 24 2016 · National One-Eighth Premium

Maximum value of $y=5\sin(x+30^\circ)+2$

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Sub-topic 25 2016 · National One-Eighth Premium

Maximum value of $y=2-5\cos(x-30^\circ)$

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Sub-topic 26 2016 · National One-Eighth Premium

Maximum value of $y=5+3\cos(30^\circ-x)$

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Sub-topic 27 2019 · National Preliminary Premium

Greatest value of $3\sin x+4\cos x$

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Sub-topic 28 2021 · National Quarterfinal Premium

Does $y=\sin(2x)$ have a maximum at $x=\dfrac{\pi}{2}$? (true/false)

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Sub-topic 29 2021 · National Quarterfinal Premium

Does $y=\cos(x)$ have a minimum at $x=\dfrac{\pi}{2}$? (true/false)

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Sub-topic 30 2021 · National Quarterfinal Premium

Does $y=\cos(2x)$ have a maximum at $x=\pi$? (true/false)

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Sub-topic 31 2022 · National Preliminary Premium

Sine and cosine are both negative in the third quadrant (true/false)

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Sub-topic 32 2022 · National Preliminary Premium

Cosine positive and sine negative in the second quadrant (true/false)

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Sub-topic 33 2022 · National Preliminary Premium

Tangent and cosine are both negative in the second quadrant (true/false)

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