A pendulum of length 1.5 m swings through a small angle θ \theta\,θ radians from the vertical.
The horizontal displacement of the pendulum bob from the vertical is x x\,x metres, where x=1.5sinθx = 1.5\sin\thetax=1.5sinθ.
The vertical rise of the bob above its lowest point is h h\,h metres, where h=1.5(1−cosθ)h = 1.5(1 - \cos\theta)h=1.5(1−cosθ).
Use small angle approximations to show that, for small θ\thetaθ,
h≈x23\displaystyle h \approx \frac{x^2}{3}h≈3x2
Use this result to estimate the vertical rise of the bob when its horizontal displacement is 0.12 m.
State one reason why this approximation would be unreliable for a horizontal displacement of 1.2 m.
317 exam-style questions on OCR (MEI) A Level Maths 1.7 Trigonometry, covering 1.7.1 Solve right-angled triangles, 1.7.2 Definitions of sin, cos and tan for any angle, 1.7.3 Graphs of sin, cos and tan, 1.7.4 Exact values of trig functions (degrees), 1.7.5 Area of a triangle, 1.7.6 Sine and cosine rules, 1.7.7 Identity tan = sin/cos, 1.7.8 Identity sin^2 + cos^2 = 1, 1.7.9 Solve simple trigonometric equations, 1.7.10 Exact values of trig functions (radians) (A-level only), 1.7.11 Inverse trigonometric functions (A-level only), 1.7.12 Radians and degree conversion (A-level only), 1.7.13 Arc length and area of a sector (A-level only), 1.7.14 Small angle approximations (A-level only), 1.7.15 Sec, cosec and cot functions (A-level only), 1.7.16 Graphs of reciprocal trig functions (A-level only), 1.7.17 Pythagorean identities for sec and cosec (A-level only), 1.7.18 Compound angle formulae (A-level only), 1.7.19 Double angle identities (A-level only), 1.7.20 Expressions for a cos θ ± b sin θ (A-level only), 1.7.21 Use identities to solve equations (A-level only), 1.7.22 Proofs involving trigonometric functions (A-level only), 1.7.23 Trig to solve problems in context (A-level only), and 1.7 Trigonometry. Each one has a worked solution and a mark scheme showing where the marks go.