During a lab experiment, the lateral displacement LLL (in cm) of a precision pendulum is recorded relative to its resting position for small angular displacements α\alphaα (in radians). The relationship is modeled by:
L(α)=14.2+25sin(α5)+12tan(α4) L(\alpha) = 14.2 + 25\sin\left(\frac{\alpha}{5}\right) + 12\tan\left(\frac{\alpha}{4}\right) L(α)=14.2+25sin(5α)+12tan(4α)Show that for small values of α\alphaα, the graph of LLL can be approximated by a straight line, and determine the equation of this line.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
