Question

Determine two pairs of polar coordinates for (4,4) when 0 degrees < theta < 360 degrees.

Answer 1

A

Explanation:

Answer 2

`\left(+4√(2), 45^(\circ)\right)` and
`\left(-4√(2), 225^(\circ)\right)`

Explanation:

The magnitude of the polar coordinates is given by the Pythagorean Theorem:

`r = \sqrt{4^(2)+4^(2)}`

`r = \sqrt{2^(5)}`

`r = 4√(2)`

One direction of the point with respect to the origin is:

`\theta = \tan^(-1)\left((4)/(4) \right)`

`\theta = 45^(\circ)`

The antiparallel version of the point is:

`r = -4√(2)`

`\theta = 225^(\circ)`

The two pairs of polar coordinates are:

`\left(+4√(2), 45^(\circ)\right)` and
`\left(-4√(2), 225^(\circ)\right)`