Question

Given R = 10 and theta = 1.15 pi, find the Cartesian coordinates. ​

Answer 1

We have been given that
`r=10` and
`\theta =1.15\pi`. We are asked to find the Cartesian coordinates.

We know that
`x=r\cdot \text{cos}(\theta)` and
`y=r\cdot \text{sin}(\theta)`.

Let us convert polar coordinates to Cartesian coordinates using above formula.

`x=10\cdot \text{cos}(1.15\pi)`

`x=10\cdot (-0.891006524188)`

`x=-8.91006524188`

Round to nearest hundredths:

`x\approx -8.91`

`y=10\cdot \text{sin}(1.15\pi)`

`y=10\cdot (-0.45399049974)`

`y=-4.5399049974`

Round to nearest hundredths:

`y\approx -4.54`

Therefore, the Cartesian coordinates will be
`(-8.91,-4.54)` and option 'b' is the correct choice.