$\displaystyle {O}{C}{B}$ is a semicircle with centre $\displaystyle {D}$ and radius $\displaystyle {a}$ , $\displaystyle {O}\hat{{{B}}}{C}=\theta$  and $\displaystyle {O}\hat{{{C}}}{B}={90}^{\circ}$ 

Question 1

Show that $\displaystyle {B}{C}={2}{a}{\cos{{\left(\theta\right)}}}$

In $\displaystyle \Delta{O}{C}{B}$

 Preview Question 6 Part 1 of 5  

$\displaystyle {B}{C}=$ Preview Question 6 Part 2 of 5  

(2)

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Question 2

If the area of $\displaystyle \Delta{O}{C}{B}={2}{a}{\sin{{\left({2}\theta\right)}}}$ , determine the coordinates of $\displaystyle {C}$ such that the area of $\displaystyle \Delta{O}{C}{B}$ is a maximum.

Area of $\displaystyle \Delta{O}{C}{B}$ will have a maximum when $\displaystyle \theta$ is $\displaystyle ^\circ$

Therefor the coordinates for $\displaystyle {C}$ will be $\displaystyle {(}$ $\displaystyle ,$ $\displaystyle {)}$

 (3)

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