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Differentiation

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Question 414

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

A robotic arm's reach RRR (measured in cm) from a central hub is modeled by the equation

R(t)=3+2cos⁡t2+sin⁡t,0≤t≤2π R(t) = \frac{3 + 2 \cos t}{2 + \sin t}, \quad 0 \le t \le 2\pi R(t)=2+sint3+2cost​,0≤t≤2π

where t t\,t is the time in seconds. A technician identifies a point in time M M\,M when the reach is at its absolute minimum.

a.

Show that the value of t t\,t at M M\,M is a solution of the equation

4sin⁡t+3cos⁡t=−2 4 \sin t + 3 \cos t = -2 4sint+3cost=−2
[4]
b.

Hence find, to 3 significant figures, the value of t t\,t at the point MMM.

[4]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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