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1.7 Trigonometry

1.7 Trigonometry

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Question 169

An automated deep-sea submersible is programmed to perform vertical transects for water sampling. Its depth, HHH metres below the surface, is recorded at various times ttt hours after its deployment at midnight. The data points collected are used to create the following model:

H=7.4cos⁡(2π(t−3.2)18)+12.5 H = 7.4 \cos\left( \frac{2\pi(t - 3.2)}{18} \right) + 12.5 H=7.4cos(182π(t−3.2)​)+12.5
a.

Find the minimum depth below the surface reached by the submersible, according to the model. Give your answer to the nearest centimetre.

[2]
b.

Find the duration of the longest continuous period during the first day (from t=0t=0t=0 to t=24t=24t=24) where the depth of the submersible is predicted to be less than 8 metres. Give your answer in hours to one decimal place.

[4]
c.

A different model is needed for a second submersible exploring a deeper trench. This second submersible exhibits a more stable vertical movement (a smaller vertical range) around the same average depth. A technician suggests refining the existing model for this second submersible by increasing the value of 7.4 to 8.2. Explain whether this refinement is appropriate.

[2]
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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