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1.7 Trigonometry

1.7 Trigonometry

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Question 173
a.

Express 8sin⁡x−15cos⁡x8 \sin x - 15 \cos x8sinx−15cosx in the form Rsin⁡(x−α)R \sin(x - \alpha)Rsin(x−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 function ggg is defined by

g(θ)=15+8sin⁡(3θ−π4)−15cos⁡(3θ−π4),θ>0 g(\theta) = 15 + 8 \sin\left(3\theta - \frac{\pi}{4}\right) - 15 \cos\left(3\theta - \frac{\pi}{4}\right), \quad \theta > 0 g(θ)=15+8sin(3θ−4π​)−15cos(3θ−4π​),θ>0

Find (i) the minimum value of g(θ)g(\theta)g(θ) (ii) the smallest value of θ\thetaθ at which this minimum value occurs.

[3]
c.

The function hhh is defined by

h(β)=5−(8sin⁡β−15cos⁡β)2 h(\beta) = 5 - (8 \sin \beta - 15 \cos \beta)^2 h(β)=5−(8sinβ−15cosβ)2

Find the range of hhh.

[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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