The displacement ddd of a mechanical oscillator is modeled by the equation
d=0.9cos(1.5t)−4.0sin(1.5t) d = 0.9 \cos(1.5t) - 4.0 \sin(1.5t) d=0.9cos(1.5t)−4.0sin(1.5t)where ddd is measured in millimetres and ttt is time in seconds. To analyze the peak amplitude of the oscillation, the expression is rewritten in the form Rcos(1.5t+α)R \cos(1.5t + \alpha)Rcos(1.5t+α), where R>0R > 0R>0.
Find the value of RRR.
Circle the correct answer from the options below:
3.13.13.1 \qquad 4.054.054.05 \qquad 4.14.14.1 \qquad 4.94.94.9
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.