We have been given that [tex]r=10[/tex] and [tex]\theta =1.15\pi[/tex]. We are asked to find the Cartesian coordinates.
We know that [tex]x=r\cdot \text{cos}(\theta)[/tex] and [tex]y=r\cdot \text{sin}(\theta)[/tex].
Let us convert polar coordinates to Cartesian coordinates using above formula.
[tex]x=10\cdot \text{cos}(1.15\pi)[/tex]
[tex]x=10\cdot (-0.891006524188)[/tex]
[tex]x=-8.91006524188[/tex]
Round to nearest hundredths:
[tex]x\approx -8.91[/tex]
[tex]y=10\cdot \text{sin}(1.15\pi)[/tex]
[tex]y=10\cdot (-0.45399049974)[/tex]
[tex]y=-4.5399049974[/tex]
Round to nearest hundredths:
[tex]y\approx -4.54[/tex]
Therefore, the Cartesian coordinates will be [tex](-8.91,-4.54)[/tex] and option 'b' is the correct choice.
