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1.7 Trigonometry

1.7 Trigonometry

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Question 78
i.

The orientation angle ϕ \phi\,ϕ of a precision solar tracker satisfies the equation

5sin⁡(ϕ−60∘)+12cos⁡(ϕ−60∘)=0 5 \sin(\phi - 60^\circ) + 12 \cos(\phi - 60^\circ) = 0 5sin(ϕ−60∘)+12cos(ϕ−60∘)=0

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

[3]
ii a.

Show that the equation

3sin⁡3α=10sin⁡α−7sin⁡αcos⁡α 3 \sin^3 \alpha = 10 \sin \alpha - 7 \sin \alpha \cos \alpha 3sin3α=10sinα−7sinαcosα

can be expressed in the form

sin⁡α(kcos⁡2α+mcos⁡α+n)=0 \sin \alpha (k \cos^2 \alpha + m \cos \alpha + n) = 0 sinα(kcos2α+mcosα+n)=0

where k,m k, m\,k,m and n n\,n are constants to be determined.

[3]
ii b.

Hence find the exact solutions of the equation

3sin⁡3α=10sin⁡α−7sin⁡αcos⁡α 3 \sin^3 \alpha = 10 \sin \alpha - 7 \sin \alpha \cos \alpha 3sin3α=10sinα−7sinαcosα

for −π≤α≤π-\pi \le \alpha \le \pi−π≤α≤π.

[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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