Find the area of the shaded region, in terms of θ.

The area of the shaded region is 12 cm². Find the value of θ.

valid approach to find area of segment      (M1)

eg  area of sector – area of triangle, \(\frac{1}{2}{r^2}\left( {\theta  - {\text{sin}}\theta } \right)\)

correct substitution      (A1)

eg  \(\frac{1}{4}{\left( 4 \right)^2}\theta  - \frac{1}{2}{\left( 4 \right)^2}{\text{sin}}\theta ,\,\,\frac{1}{2} \times 16\left[ {\theta  - {\text{sin}}\theta } \right]\)

area = 80 – 8 sinθ, 8(θ – sinθ)     A1 N2

[3 marks]

setting their area expression equal to 12      (M1)

eg  12 = 8(θ – sinθ)    

2.26717

θ = 2.27 (do not accept an answer in degrees)      A2 N3

[3 marks]