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Question 55

The deflection $D$ of a micro-cantilever, in micrometres, is modelled for small tilt angles $θ\theta$ (measured in radians) by the expression

\cos 4\theta + 3 \sin 2\theta - \tan 5\theta

Show that, for small values of $θ\theta$ , the deflection can be approximated by the quadratic form

Q\theta + R\theta^2

where $P$ , $Q$ and $R$ are constants to be found.

[4]

Use your answer to part (a) to find an approximation for the deflection when

\cos 0.16 + 3 \sin 0.08 - \tan 0.20

Give your answer to three decimal places.

[3]

Markscheme

Radians Questions

A Level
Maths
Radians

69 exam-style questions on Edexcel A Level Maths Radians, covering 5.1 Radian Measure, 5.2 Arc Length, 5.3 Areas of Sectors and Segments, 5.4 Solving Trigonometric Equations, and 5.5 Small Angle Approximations. Each one has a worked solution and a mark scheme showing where the marks go.

Radians

Question bank

Radians

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Question 55

The deflection $D$ of a micro-cantilever, in micrometres, is modelled for small tilt angles $θ\theta$ (measured in radians) by the expression

\cos 4\theta + 3 \sin 2\theta - \tan 5\theta

Show that, for small values of $θ\theta$ , the deflection can be approximated by the quadratic form

Q\theta + R\theta^2

where $P$ , $Q$ and $R$ are constants to be found.

[4]

Use your answer to part (a) to find an approximation for the deflection when

\cos 0.16 + 3 \sin 0.08 - \tan 0.20

Give your answer to three decimal places.

[3]

Markscheme

Radians Questions

A Level
Maths
Radians