Question

use the circle shown in the rectangular coordinate system to draw an angle of 510° in standard position. state the quadrant in which the angle lies. choose the figure below that shows an angle of 510° in standard position. a. b. c. d. when it is in standard position, the angle lies in

Explanation:

Step1: Find a coterminal angle

To find a coterminal angle of \(510^{\circ}\) between \(0^{\circ}\) and \(360^{\circ}\), subtract \(360^{\circ}\) from \(510^{\circ}\).
\(510 - 360=150^{\circ}\)

Step2: Determine the quadrant

An angle \(\theta\) with \(90^{\circ}<\theta < 180^{\circ}\) lies in the second - quadrant. Since \(150^{\circ}\) is between \(90^{\circ}\) and \(180^{\circ}\), the angle \(510^{\circ}\) (which is coterminal with \(150^{\circ}\)) lies in the second - quadrant.

Answer:

The angle of \(510^{\circ}\) in standard position lies in the second quadrant. Without seeing the actual figures A, B, C, D, we can't choose the correct figure, but the angle should have its terminal side in the second quadrant.