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1.7 Trigonometry

1.7 Trigonometry

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Question 100
i.

A mechanical sensor measures the angular misalignment α \alpha\,α of a rotating component. The misalignment follows the equilibrium condition:

6sin⁡(α−35∘)=−5cos⁡(α−35∘) 6 \sin(\alpha - 35^\circ) = -5 \cos(\alpha - 35^\circ) 6sin(α−35∘)=−5cos(α−35∘)

Determine all possible values of α \alpha\,α in the range 0<α<360∘0 < \alpha < 360^\circ0<α<360∘, giving your answers to one decimal place.

[4]
ii a.

Show that the equation describing the lateral vibration of a specific piston,

5sin⁡3x=7sin⁡x−4sin⁡xcos⁡x 5 \sin^3 x = 7 \sin x - 4 \sin x \cos x 5sin3x=7sinx−4sinxcosx

can be written in the form

sin⁡x(acos⁡2x+bcos⁡x+c)=0 \sin x (a \cos^2 x + b \cos x + c) = 0 sinx(acos2x+bcosx+c)=0

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

[3]
ii b.

Hence find all real solutions for −π≤x≤π-\pi \le x \le \pi−π≤x≤π to the equation

5sin⁡3x=7sin⁡x−4sin⁡xcos⁡x 5 \sin^3 x = 7 \sin x - 4 \sin x \cos x 5sin3x=7sinx−4sinxcosx

giving your answers to two decimal places where appropriate.

[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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