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1.7 Trigonometry

1.7 Trigonometry

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Question 68

Let f(θ)=3cos⁡θ−6sin⁡θf(\theta) = 3\cos\theta - 6\sin\thetaf(θ)=3cosθ−6sinθ for θ∈R\theta \in \mathbb{R}θ∈R.

a.

Express f(θ)f(\theta)f(θ) in the form Rcos⁡(θ+α)R\cos(\theta + \alpha)Rcos(θ+α), where R>0R > 0R>0 and 0<α<π20 < \alpha < \frac{\pi}{2}0<α<2π​. Give the exact value of RRR and the value of α\alphaα, in radians, to 3 decimal places.

[3]
b.

The curve with equation y=cos⁡θy = \cos\thetay=cosθ is transformed onto the curve with equation y=f(θ)y = f(\theta)y=f(θ) by a sequence of two transformations.

Given that the first transformation is a stretch and the second is a translation:

(i) Describe fully the transformation that is a stretch. (ii) Describe fully the transformation that is a translation.

[4]
c.

Given g(θ)=755+(f(θ))2g(\theta) = \frac{75}{5 + (f(\theta))^2}g(θ)=5+(f(θ))275​, find the range of ggg.

[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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