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

Answer:

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

Step-by-step explanation:

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

$\theta = \pi\,rad + \tan^{-1} \left(\frac{3\sqrt{2}}{12} \right)$

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

$\theta \approx 1.108\pi\,rad$

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