91Ó°ÊÓ

Convert the given angle to radians. \(15^{\circ}\)

A central angle in a circle of radius \(2 \mathrm{~cm}\) cuts off an arc of length \(4.6 \mathrm{~cm}\). What is the measure of the angle in radians? What is the measure of the angle in degrees?

Put your calculator in radian mode and take the cosine of \(0 .\) Whatever the answer is, take its cosine. Then take the cosine of the new answer. Keep repeating this. On most calculators after about \(50-60\) iterations you should start to see the same answer repeating. What is that number? Try starting with a number different from \(0 .\) Do you get the same answer repeating after roughly the same number of iterations as before? Try the same procedure in degree mode, starting with \(0^{\circ}\). Does the same thing happen? If so, does it take fewer iterations for the answer to start repeating than in radian mode, or more?

Find the perimeter of a regular dodecagon (i.e. a 12-sided polygon with sides of equal length) inscribed inside a circle of radius \(\frac{1}{2}\). Compare it to the circumference of the circle.