SHELDON'S LOGO

Note: You should measure the diagram as it is presented.

Sheldon has designed the logo below.

The diagram shows a circle which is divided into three regions by two curves. The logo is the unshaded region between the two curves $($white section$).$ Sheldon wishes to develop mathematical functions that model these curves.

Using an appropriate set of axes, identify and record a number of data points on the curves which will allow you to develop model functions for them. Define all variables used and state any parameters clearly.

Using technology, plot these two sets of data points on a graph. What type of functions model the behaviour of the data? Explain why you chose these functions.

Find functions that represent the upper and lower curves forming the logo$.$ Discuss any limitations$.$

Sheldon wishes to print T$-$shirts with the logo on the back. He must double the dimensions of the logo for this purpose. Describe how your functions must be modified.

Sheldon also wishes to print stickers. A standard sticker has a radius of $5$ cm$.$ How must your functions be modified so that the logo fits on the sticker $($end to end$)?$ Use technology to show the results.