Question

The diagram shows the curve with equation y = ( 1 + x ) cosx.

Complete the table below for points on the curve, giving the y values correct to 3 decimal places where appropriate.

Answer 1

y = 1, 1.319, 1.024, 0

Explanation:

Given equation:

`y=(1+x)\cos x`

`\textsf{when}\:x=0:`

`\begin{aligned} \implies y & =(1+0)\cos 0\\\implies y & = 1\end{aligned}`

`\textsf{when}\:x=(\pi)/(6):`

`\begin{aligned} \implies y & =\left(1+(\pi)/(6)\right)\cos \left((\pi)/(6)\right)\\\implies y & = 1.319\: \sf (3\:dp)\end{aligned}`

`\textsf{when}\:x=(\pi)/(3):`

`\begin{aligned} \implies y & =\left(1+(\pi)/(3)\right)\cos \left((\pi)/(3)\right)\\\implies y & = 1.024\: \sf (3\:dp)\end{aligned}`

`\textsf{when}\:x=(\pi)/(2):`

`\begin{aligned} \implies y & =\left(1+(\pi)/(2)\right)\cos \left((\pi)/(2)\right)\\\implies y & = 0\end{aligned}`