<p>The parametric equations of a curve $C$ are $x=1-\sin t$ and $y=\cos t$, $0\le t\le 2\pi $.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find $\frac{\mathrm{d}y}{\mathrm{d}x}$.</span></div><p style="text-align: right;">[1]</p></li><li><div class="list-item-content"><span class="list-item-text">Find the exact value(s) of $t$ at the point when the tangent is parallel to the $y$-axis.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">Show that the equation of the normal at the point with parameter $p$ is $y=-x\cot p+\cot p$.</span></div><p style="text-align: right;">[2]</p></li><li><div class="list-item-content"><span class="list-item-text">Show that the normal at the point $A$ with coordinates $\left( 1-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right)$ cuts the curve again at another point $B$. Find the coordinates of $B$.</span></div><p style="text-align: right;">[2]</p></li></ol>

The parametric equations of a curve $C$ are $x=1-\sin t$ and $y=\cos t$, $0\le t\le 2\pi $.

Find the exact value(s) of $t$ at the point when the tangent is parallel to the $y$-axis.

Show that the equation of the normal at the point with parameter $p$ is $y=-x\cot p+\cot p$.

Show that the normal at the point $A$ with coordinates $\left( 1-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right)$ cuts the curve again at another point $B$. Find the coordinates of $B$.

ACJC Tutorial 13 Q1

ACJC Tutorial 13 Q1

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