Find ${\rm{A\hat OB}}$, expressing your answer in radians correct to four significant figures.

Determine the area of the shaded region.

EITHER

${\rm{A\hat OB}} = 2\arcsin \left( {\frac{3}{4}} \right)$ or equivalent (eg ${\rm{A\hat OB}} = 2\arctan \left( {\frac{3}{{\sqrt 7 }}} \right),{\rm{ A\hat OB}} = 2\arccos \left( {\frac{{\sqrt 7 }}{4}} \right)$)     (M1)

OR

$\cos {\rm{A\hat OB}} = \frac{{{4^2} + {4^2} - {6^2}}}{{2 \times 4 \times 4}}{\text{ }}\left( { =  - \frac{1}{8}} \right)$     (M1)

THEN

$= 1.696$ (correct to 4sf)     A1

[2 marks]

use of area of segment = area of sector – area of triangle     (M1)

$= \frac{1}{2} \times {4^2} \times 1.696 - \frac{1}{2} \times {4^2} \times \sin 1.696$     (A1)

$= 5.63{\text{ (c}}{{\text{m}}^2})$     A1

[3 marks]

This was generally well done. In part (a), a number of candidates expressed the required angle either in degrees or in radians stated to an incorrect number of significant figures.

This was generally well done. In part (b), some candidates demonstrated a correct method to calculate the shaded area using an incorrect formula for the area of a sector.