Question

Give the radian measure of an angle drawn in standard position that corresponds with the ray containing the coordinate point (−12, −3√2).

Answer 1

The radian measure of the angle drawn in standard position that corresponds with the ray containing the coordinate point
`(-12, -3√(2))` is approximately
`1.108\pi` radians.

Explanation:

With respect to origin, the coordinate point belongs to the third quadrant, which comprises the family of angles from
`\pi\,rad` to
`(3\pi)/(2)\,rad`. The angle in standard position can be estimated by using the following equivalence:

`\theta = \pi\,rad + \tan^(-1) \left((3√(2))/(12) \right)`

`\theta \approx \pi \,rad + 0.108\pi \,rad`

`\theta \approx 1.108\pi\,rad`

The radian measure of the angle drawn in standard position that corresponds with the ray containing the coordinate point
`(-12, -3√(2))` is approximately
`1.108\pi` radians.