Question

enter the coordinates of the point on the unit circle at the given angle. - 225 ^ { \circ } ( - \frac { \sqrt { ? } } { 2 } , \frac { \sqrt { } } { 2 } )

Explanation:

Step1: Find the equivalent positive angle

Since \(-225^{\circ}+360^{\circ} = 135^{\circ}\), the angle \(-225^{\circ}\) is coterminal with \(135^{\circ}\).

Step2: Use the unit - circle coordinates formula

For a point \((x,y)\) on the unit circle \(x = \cos\theta\) and \(y=\sin\theta\). For \(\theta=- 225^{\circ}\) (or \(135^{\circ}\)), \(\cos(-225^{\circ})=\cos(135^{\circ})=-\frac{\sqrt{2}}{2}\) and \(\sin(-225^{\circ})=\sin(135^{\circ})=\frac{\sqrt{2}}{2}\)

Answer:

\((-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})\)