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Differentiation

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Question 221

A curve has the parametric equations

x=tan⁡2t,y=cos⁡t,0<t<π2 x = \tan^2 t, \quad y = \cos t, \quad 0 < t < \frac{\pi}{2} x=tan2t,y=cost,0<t<2π​
a.

Find an expression for dydx\displaystyle \frac{dy}{dx}dxdy​ in terms of ttt.

[3]
b.

Find the coordinates of the point on the curve when t=π4\displaystyle t=\frac{\pi}{4}t=4π​.

[2]
c.

Hence find an equation of the tangent to the curve when t=π4\displaystyle t=\frac{\pi}{4}t=4π​.

[3]
d.

Find a cartesian equation for the curve.

[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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