5. (a) Sketch the graph of \(y = \sin 2 x , \quad 0 \leqslant x \leqslant \frac { 3 \pi } { 2 }\)
Show the coordinates of the points where your graph crosses the \(x\)-axis.
The table below gives corresponding values of \(x\) and \(y\), for \(y = \sin 2 x\).
The values of \(y\) are rounded to 3 decimal places where necessary.
| \(x\) | 0 | \(\frac { \pi } { 12 }\) | \(\frac { \pi } { 6 }\) | \(\frac { \pi } { 4 }\) |
| \(y\) | 0 | 0.5 | 0.866 | 1 |
(b) Use the trapezium rule with all the values of \(y\) from the table to find an approximate value for