2014 ONE(c)

Merit
Question
If x=2sin⁡tx = 2\sin t and y=cos⁡2ty = \cos 2t show that dydx=−2sin⁡t\dfrac{dy}{dx} = -2\sin t.
Official Answer
x=2sin⁡ty=cos⁡2tx=2\sin t\qquad y=\cos 2t
dxdt=2cos⁡tdydt=−2sin⁡2t\dfrac{dx}{dt}=2\cos t\qquad \dfrac{dy}{dt}=-2\sin 2t
dydx=−2sin⁡2t2cos⁡t\dfrac{dy}{dx}=\dfrac{-2\sin 2t}{2\cos t}
=−2×2sin⁡tcos⁡t2cos⁡t=\dfrac{-2\times 2\sin t\cos t}{2\cos t}
=−2sin⁡t=-2\sin t
Grading Criteria

Achievement (u)

  • Correct expressions for dxdt\dfrac{dx}{dt} and dydt\dfrac{dy}{dt}.

Merit (r)

  • A correct solution.

Excellence T1

-

Excellence T2

-
Exam Paper (2014)Assessment Schedule (2014)
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