Problem

Consider the picture below.

q is the central angle of the circle, s is the arc intercepted by q, and d is the chord defined by q. Find

Solution

We know that s = rq, where r is the radius of the circle. To find d, we redraw the section of the circle subtended by q, and include the bisector of q.

Now we have a relationship between q, r and d:

Substitute for r:

Then the limit can be written as

Following the argument in Example 1 in section 2.9 of the textbook, the value of this limit equals 1.