Question

Convert the following point from polar to Cartesian coordinates. Write the exact answer as an ordered pair. Do not round.✓(4, 5),704

Answer 1

Polar Coordinates

Given a point in coordinates (r, θ), the equivalent point in cartesian coordinates (x, y) can be found as:

x = r cos θ

y = r sin θ

We are given the point:

`(4,(7\pi)/(4))`

Converting to cartesian coordinates:

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

The cartesian coordinates are:

`(2√(2),-2√(2))`