3.90: Small change for $y = \sin 5x$

0606/13/O/N/25 — Question 3 · 4 marks

You may use the values in the standard trig table for

\dfrac{\pi}{6}

and

\dfrac{\pi}{3}

Variables

x

and

y

are related by

y = \sin 5x

where

0 \leqslant x \leqslant \dfrac{\pi}{10}

Use calculus to find the approximate change in

x

when

y

increases from

\dfrac{\sqrt{3}}{2}

by the small amount

0.01

[4]

3.90: Small change for y=sin⁡5xy = \sin 5xy=sin5x