2023 TWO(b)

Achievement
Question
Find the gradient of the tangent to the curve y=cot⁡(2x)y = \cot(2x) at the point where x=π12x = \dfrac{\pi}{12}.

You must use calculus and show any derivatives that you need to find when solving this problem.
Official Answer
dydx=−2cosec⁡2(2x)\dfrac{dy}{dx}=-2\operatorname{cosec}^2(2x)

When x=π12x=\dfrac{\pi}{12}

dydx=−2sin⁡2(π6)\dfrac{dy}{dx}=\dfrac{-2}{\sin^2\left(\dfrac{\pi}{6}\right)}

=−8=-8
Grading Criteria

Achievement (u)

  • Correct derivative.
    AND
    Correct gradient of −8-8 found.

Merit (r)

-

Excellence T1

-

Excellence T2

-
Video Explanation
2023 NCEA L3 Calculus Exam Walkthrough by infinityplusone(starts at 30:10)
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Exam Paper (2023)Assessment Schedule (2023)
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