The lateral force FFF, measured in Newtons, exerted on a precision pendulum support is modeled by the function
F(θ)=14.5+54sin(θ6)−16tan(θ8) F(\theta) = 14.5 + 54 \sin \left( \frac{\theta}{6} \right) - 16 \tan \left( \frac{\theta}{8} \right) F(θ)=14.5+54sin(6θ)−16tan(8θ)where θ\thetaθ is the angular displacement from the vertical in radians. Show that, for small values of θ\thetaθ, the graph of FFF against θ\thetaθ can be approximated by a straight line, and state the equation of this line.
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.