Example  3
Given the point \((4, -6)\) on the terminal arm of an angle in standard position, determine three other points on the terminal arms of other angles in standard position that have the same reference angle.

To help solve this problem, start by plotting the point \((4, -6)\) and drawing the reference angle \(\theta_R\).

Points on the terminal arms of other angles in standard position, with the same reference angle, will be found by reflecting the original reference angle about the \(x\)-axis, and then reflecting those two angles about the \(y\)-axis.


  • \(\theta_1\) is the reflection of \(\theta_R\) about the \(x\)-axis
  • \(\theta_2\) is the reflection of \(\theta_R\) about the \(x\)-axis, followed by a reflection about the \(y\)-axis
  • \(\theta_3\) is the reflection of \(\theta_R\) about the \(y\)-axis

The points on the terminal arms of the resulting angles in standard position that have the same reference angle are \((4, 6)\), \((-4, 6)\), and \((-4, -6)\).