Question

Convert the following point from polar to Cartesian coordinates. Write the exact answer as an ordered pair. Do not round.(4.5%)

Answer 1

Given:

`\begin{gathered} (4,(7\pi)/(4)) \\ where; \\ r=4 \\ \theta=(7\pi)/(4) \end{gathered}`

To convert from polar to cartesian coordinates,

`\begin{gathered} x=rcos\theta \\ y=rsin\theta \end{gathered}`
`\begin{gathered} x=4cos(7\pi)/(4) \\ x=(4√(2))/(2) \\ x=2√(2) \end{gathered}`
`\begin{gathered} y=4sin(7\pi)/(4) \\ y=4((-√(2))/(2)) \\ y=-2√(2) \end{gathered}`

Hence, the pair as a cartesian coordinate as an ordered pair is;

`(2√(2),-2√(2))`