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1.7 Trigonometry

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Question 54

A specialized sonar sensor calculates the angle of reflection α\alphaα, in radians, from a submerged object at distance xxx meters using the model:

α(x)=arcsin⁡(2x−115) \alpha(x) = \arcsin\left(\frac{2x - 11}{5}\right) α(x)=arcsin(52x−11​)

Determine the maximum possible domain of α\alphaα.

Select the correct option:

  1. {x∈R:3≤x≤8}\{x \in \mathbb{R} : 3 \le x \le 8\}{x∈R:3≤x≤8}
  2. {x∈R:−1≤x≤1}\{x \in \mathbb{R} : -1 \le x \le 1\}{x∈R:−1≤x≤1}
  3. {x∈R:−π2≤α≤π2}\{x \in \mathbb{R} : -\frac{\pi}{2} \le \alpha \le \frac{\pi}{2}\}{x∈R:−2π​≤α≤2π​}
  4. {x∈R:3<x<8}\{x \in \mathbb{R} : 3 < x < 8\}{x∈R:3<x<8}
[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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