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1.8.6 Compound and double angle formulae (A-level only)

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Question 21

The angular displacement, $ϕ\phi$ , of a high-precision robotic arm relative to its equilibrium position is modelled by the equilibrium state equation:

\sec \phi = 32 \sin \phi

Show that this equation can be expressed in the form $sin⁡2ϕ=k\sin 2\phi = k$ , where $k\,$ is a constant to be determined.

[4]

Hence, find the smallest positive value of $ϕ\phi$ , in degrees, that satisfies this equilibrium state. Give your answer to one decimal place.

[3]

Markscheme

1.8.6 Compound and double angle formulae (A-level only) Questions

A Level
Maths
1.8.6 Compound and double angle formulae (A-level only)

46 exam-style questions on AQA A Level Maths 1.8.6 Compound and double angle formulae (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

1.8.6 Compound and double angle formulae (A-level only)

Question bank

1.8.6 Compound and double angle formulae (A-level only)

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Question 21

The angular displacement, $ϕ\phi$ , of a high-precision robotic arm relative to its equilibrium position is modelled by the equilibrium state equation:

\sec \phi = 32 \sin \phi

Show that this equation can be expressed in the form $sin⁡2ϕ=k\sin 2\phi = k$ , where $k\,$ is a constant to be determined.

[4]

Hence, find the smallest positive value of $ϕ\phi$ , in degrees, that satisfies this equilibrium state. Give your answer to one decimal place.

[3]

Markscheme

1.8.6 Compound and double angle formulae (A-level only) Questions

A Level
Maths
1.8.6 Compound and double angle formulae (A-level only)

46 exam-style questions on AQA A Level Maths 1.8.6 Compound and double angle formulae (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.