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1.7 Trigonometry

1.7 Trigonometry

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Question 104

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

i.

Solve, for 0<x⩽π0 < x \leqslant \pi0<x⩽π, the equation

6sin⁡xtan⁡x+5=2cos⁡x 6 \sin x \tan x + 5 = 2 \cos x 6sinxtanx+5=2cosx

giving your answer in radians to 3 significant figures.

[4]
a.

The dissolved oxygen concentration, DDD mg/L, in a fish pond ttt hours after midnight is modelled by the equation

D=15+10sin⁡(kt−35)∘0⩽t<24 D = 15 + 10 \sin(kt - 35)^\circ \quad 0 \leqslant t < 24 D=15+10sin(kt−35)∘0⩽t<24

where kkk is a constant. Use the equation of the model to answer parts (a) to (c).

Given that

  • the dissolved oxygen concentration was 202020 mg/L at 8 am
  • 0<k<300 < k < 300<k<30

Find all possible values for kkk, giving each answer to 2 decimal places.

[4]
b.

Given further that 0<k<150 < k < 150<k<15

Find the maximum dissolved oxygen concentration in the pond.

[1]
c.

Find the time of day at which this maximum concentration occurs. Give your answer to the nearest minute.

[2]
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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