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1.7 Trigonometry

1.7 Trigonometry

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Question 116

A sub-aquatic drone's descent angle θ \theta\,θ is controlled by a buoyancy system. To maintain stable movement, the angle must satisfy the equilibrium equation:

5cot⁡2θ+3 cosec2θ=2 cosec θ+10 5\cot^2\theta + 3\text{ cosec}^2\theta = 2\text{ cosec }\theta + 10 5cot2θ+3 cosec2θ=2 cosec θ+10
a.

Show that this equation can be written in the form

a cosec2θ+b cosec θ+c=0 a\text{ cosec}^2\theta + b\text{ cosec }\theta + c = 0 a cosec2θ+b cosec θ+c=0

where aaa, bbb, and c c\,c are integers to be found.

[3]
b.

Hence, given that the drone is tilted at an obtuse angle θ \theta\,θ that satisfies this stability equation, determine the exact value of tan⁡θ\tan \thetatanθ. Fully justify your answer.

[4]
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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