2020 VJC J1 MYE Q7
A curve $C$ has parametric equations
$x=\sin t-\frac{1}{2}t,$ $y=\cos t,$ for $0<t<\pi $
(i)
Show that the equation of the normal to $C$ at the point with parameter $t$ may be expressed as
$y\sin t=\left( \cos t-\frac{1}{2} \right)\left( x+\frac{1}{2}t \right)+\frac{1}{2}\sin t.$
[4]
(ii)
Determine the exact coordinates of the points on $C$ whose normal pass through the point $\left( -\frac{\pi }{4},\frac{1}{2} \right).$
[4]
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