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1.7 Trigonometry

1.7 Trigonometry

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Question 196

The vertical displacement of a specialized laboratory sensor, VVV, is modelled by the function V(θ)=8cos⁡θ+15sin⁡θV(\theta) = 8\cos \theta + 15\sin \thetaV(θ)=8cosθ+15sinθ, where θ\thetaθ is the phase angle in radians.

a.

Express V(θ)V(\theta)V(θ) in the form Rcos⁡(θ−α)R\cos(\theta - \alpha)Rcos(θ−α), where R>0R > 0R>0 and 0<α<π20 < \alpha < \frac{\pi}{2}0<α<2π​. Give the exact value of RRR and the value of α\alphaα, in radians, to 3 decimal places.

[3]
b.

A secondary performance metric for the sensor, H(t)H(t)H(t), is defined by H(t)=12−3V(4t)H(t) = 12 - 3V(4t)H(t)=12−3V(4t), for t≥0t \ge 0t≥0, where ttt is the time in seconds.

Using the answer to part (a), (i) determine the exact maximum value of H(t)H(t)H(t). (ii) find the smallest positive value of ttt for which this maximum value occurs, giving your answer to 2 decimal places.

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Markscheme

1.7 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.7 Trigonometry

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.

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