Sine and cosine derivatives
Sine and cosine derivatives
7 marks
TGM Original
Angles are in radians. Given y=2 x + cos(2 x), find dydx. Hence find its value at x= pi6. Find all zero-gradient inputs in 0 <= x <= pi.
Solution:
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Answer:\(\dfrac{\mathrm{d}y}{\mathrm{d}x}=2 - 2 \sin{\left(2 x \right)}\); at \(x=\dfrac{\pi}{6}\), \(2 - \sqrt{3}\). The required input is \(x=\dfrac\pi4\).
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