Target Mathematics

1.92: Estimate roots using a graph

4PM1/2/January/2015 — Question 5 · 8 marks

1.92 diagram 1
The grid opposite shows the graph of y=3xsinxy=3x\sin x for 1x3-1\le x\le3, where xx is measured in radians.
(a) Use the graph to estimate, to 1 decimal place, the roots of the equation xsinx=1x\sin x=1 in the interval 1x3-1\le x\le3. (3)
(b) By drawing a suitable straight line on the grid, obtain estimates, to 1 decimal place, of the roots of the equation 2xsinxx=12x\sin x-x=1 in the interval 1x3-1\le x\le3. (5)