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1.7 Trigonometry

1.7 Trigonometry

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Question 185

A high-precision docking system in an aerospace facility uses two automated parallel assemblies, A A\,A and BBB, which oscillate vertically to dampen vibrations during a calibration cycle of 6π 6\pi\,6π minutes. At time t t\,t minutes after the cycle begins, the height hA h_A\,hA​ metres of assembly A A\,A above the hangar floor is given by

hA=26.8−7sin⁡t h_A = 26.8 - 7\sin t hA​=26.8−7sint

At time t t\,t minutes after the cycle begins, the height hB h_B\,hB​ metres of assembly B B\,B above the hangar floor is given by

hB=7.4−5cos⁡t h_B = 7.4 - 5\cos t hB​=7.4−5cost
a.

Show that the initial vertical separation between assembly A A\,A and assembly B B\,B is 24.4 metres.

[3]
b.

Show that the distance Δ \Delta\,Δ metres between the two assemblies at time t t\,t is given by

Δ=19.4+Rcos⁡(t+α) \Delta = 19.4 + R\cos(t + \alpha) Δ=19.4+Rcos(t+α)

where R R\,R and α \alpha\,α are positive constants to be found. Give R R\,R in surd form and α \alpha\,α in radians to two decimal places.

[4]
c.

Hence, determine the minimum vertical distance between the two assemblies. Give your answer to the nearest centimetre.

[3]
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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