Show that, for small angles expressed in radians, the fractional error in replacing…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Show that, for small angles expressed in radians, the fractional error in replacing

\sin\theta

\theta

is approximately

\theta^{2}/6

. Hence find this fractional error when

\theta = 0.10\,\text{rad}