Question

Find the x'y coordinates for the given point and the given angle of rotation, 0. Enter the exact answer or round to four decimal places, if necessary.(-13 ) 0 - 1 / 1.30 =4

Answer 1

Given:

The point is

`(x,y)=(-7.3,-(2)/(3))`

The angle of rotation is,

`\theta=(\pi)/(4)`

Required:

To find the coordinate of x'y'.

Step-by-step explanation:

Now

`y^(\prime)=y\cos\theta+x\sin\theta`
`=-(2)/(3)\cos(\pi)/(4)+(-7.3)\sin(\pi)/(4)`
`\begin{gathered} =-(2)/(3)(0.7071)+7.3(0.7071) \\ \\ =-0.4714-5.16183 \\ \\ =-5.633 \end{gathered}`
`x^(\prime)=-y\sin\theta+x\cos\theta`
`\begin{gathered} =(2)/(3)(0.7071)-7.3(0.7071) \\ \\ =-4.69 \end{gathered}`

Final Answer:

`(x^(\prime),y^(\prime))=(-4.69,-5.633)`