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1.7 Trigonometry

1.7 Trigonometry

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Question 208

The angle of rotation ψ\psiψ of a high-precision robotic arm, where 0<ψ<π0 < \psi < \pi0<ψ<π, is determined by the following equilibrium equation:

4cot⁡2ψ+2=4csc⁡ψ+13 4\cot^2 \psi + 2 = 4\csc \psi + 13 4cot2ψ+2=4cscψ+13
a.

Show that the equation can be written in the form

acsc⁡2ψ+bcsc⁡ψ+c=0 a\csc^2 \psi + b\csc \psi + c = 0 acsc2ψ+bcscψ+c=0

where aaa, bbb, and ccc are integers to be found.

[3]
b.

Hence, given that the robotic arm is positioned at an obtuse angle ψ\psiψ that satisfies the original equation, find the exact value of tan⁡ψ\tan \psitanψ. 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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