Question

Convert the following point from polar to Cartesian coordinates. Write the exact answer as an ordered pair. Do not round.e(-3. - ?)2103

Answer 1

`((3)/(2),(3√(3))/(2))`

Step-by-step explanation

a coordiante given in polar form is has the structure

`\begin{gathered} \langle r,\theta\rangle \\ whe\text{re r is the magnitude of the vector} \\ \theta\text{ is the angle with the positive x-axis} \end{gathered}`

now, to convert from polar to Cartesian coordiantes we need to apply the formula

`\begin{gathered} x-coordinate\text{= r*cos }\theta \\ y-coordinater\text{= r}*\sin\theta \end{gathered}`

Step 1

`(-3,-(2\pi)/(3))`

so,

a)b)let

`\begin{gathered} r=-3 \\ \theta=(-2\pi)/(3) \end{gathered}`

b)Now,replace

`\begin{gathered} x-coordiante=r*cos\text{ }\theta \\ x-coordiante=-3*cos((-2\pi)/(3))= \\ x-coordiante=-3*-0.5=1.5 \\ x-coordiante=1.5 \end{gathered}`

c) y-coordinate

`\begin{gathered} y-coordinate=r*sin\theta \\ replace \\ y-continent=-3*\sin((-2\pi)/(3)) \\ y-continent=-3*-(√(3))/(2) \\ y-continent=(3√(3))/(2) \end{gathered}`

so, the answer is

`((3)/(2),(3√(3))/(2))`

I hope this helps you