Skip to content

Course home

1.5 Trigonometry

1.5 Trigonometry

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209
Question 172

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

1.5 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Trigonometry

317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank