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1.7 Trigonometry

1.7 Trigonometry

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Question 87

The temperature, θ\thetaθ °C, inside a warehouse is modelled by the equation

θ=8+2sin⁡(15t−160)°+3cos⁡(15t−160)°\theta = 8 + 2\sin(15t - 160)° + 3\cos(15t - 160)°θ=8+2sin(15t−160)°+3cos(15t−160)°

where t t\,t is the number of hours after midnight.

a.

Express 2sin⁡x+3cos⁡x2\sin x + 3\cos x2sinx+3cosx in the form Rsin⁡(x+α)R\sin(x + \alpha)Rsin(x+α), where R>0 R > 0\,R>0 and 0°<α<90°0° < \alpha < 90°0°<α<90°. Give R R\,R to three significant figures and α \alpha\,α to two decimal places.

[3]
b.

Deduce the maximum temperature inside the warehouse during the day.

[1]
c.

Find the time of day at which this maximum temperature occurs, giving your answer to the nearest minute.

[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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