(Solved): 7. A rectangle inscribed in a circle of radius 5 is determined by the angle \( \theta \) as shown ...

7. A rectangle inscribed in a circle of radius 5 is determined by the angle \( \theta \) as shown below. (a) Show that the area of the rectangle is given by the formula \( A=50 \sin (2 \theta) \) (b) What is the maximum of \( f(\theta)=\sin (2 \theta) \) (c) Determine the maximum area possible for a rectangle inscribed as above. (d) What value of \( \theta \) is necessary to achieve the maximum?