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1.7 Trigonometry

1.7 Trigonometry

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Question 174

In the study of oscillatory motion, the angular displacement of a mechanical sensor is determined to be zero when the tilt angle β\betaβ satisfies the equation

16cos⁡β=5.2cosec⁡β 16 \cos \beta = 5.2 \operatorname{cosec} \beta 16cosβ=5.2cosecβ

where 0∘<β<90∘0^\circ < \beta < 90^\circ0∘<β<90∘.

a.

Show that this equation can be expressed in the form

sin⁡2β=k \sin 2\beta = k sin2β=k

where kkk is a constant to be determined.

[4]
b.

Hence determine the smallest positive value of β\betaβ, giving your answer in degrees to one decimal place.

[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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