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.