In this task you are required to make use of trigonometric functions, research and use the Monte Carlo method of integration to determine areas under curves and perform calculations on your results.

Note: The scale on the horizontal axis 1radian = 1cm.

Your father has decided to give your mother a belated Valentines gift of a gold and pearl pendant and asked you to design one for her. Your father has the following instructions for the jeweller:

1.  The pendant must be between 3 and 4 cm (inclusive) in length and 3 cm wide.

2.  The gold should have a thickness of 4 mm.

3.  The pearl must have a diameter of 1 cm. 

You have experimented with various functions on your calculator and have decided on the following design: 

Your father is concerned about the cost of the gold in the pendant and has asked you to estimate the area of gold in the pendant. Using technology accurately graph the functions that match the designs and label the graphs.