Problem

When solving problems in geometric optics, engineers and physicists often use the simplifying assumption that, for small angles q, sin(q) is approximately equal to q.

Find a linear approximation for sin(x) that shows why this is a reasonable assumption.

Solution

Let f(x) = sin(x). We will consider small angles q, so the linear approximation will be about a = 0.

thus

Therefore near q = 0, sin(q) is approximately equal to q.