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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 731

A curve has the parametric equations

x=tan⁡2tx = \tan^2 tx=tan2t, y=cos⁡ty = \cos ty=cost, where 0<t<π2\displaystyle 0 < t < \frac{\pi}{2}0<t<2π​

a.

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

[3]
b.

Find an equation for the tangent to the curve at the point where t=π4\displaystyle t = \frac{\pi}{4}t=4π​.

[4]
Markscheme

3 Unit A2 1: Pure Mathematics (A-level only) Questions

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