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1.7 Trigonometry

1.7 Trigonometry

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Question 166
a.

Express 7cos⁡θ+5sin⁡θ7\cos \theta + 5\sin \theta7cosθ+5sinθ 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.

A researcher is monitoring the light intensity in a controlled growth chamber. The intensity, III units, is modeled by the equation

I=10012+7cos⁡(0.25t)+5sin⁡(0.25t),0≤t≤24 I = \frac{100}{12 + 7\cos(0.25t) + 5\sin(0.25t)}, \quad 0 \le t \le 24 I=12+7cos(0.25t)+5sin(0.25t)100​,0≤t≤24

where ttt is the number of hours since the start of the growth cycle.

Using the model, determine: the minimum light intensity measured in the chamber, giving your answer to 2 decimal places,

[3]
c.

the value of ttt, to 2 decimal places, when the light intensity first reaches 6.5 units.

[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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