Question

enter the coordinates of the point on the unit circle at the given angle. - 180 ^ { \circ } (?, )

Explanation:

Step1: Recall the unit - circle coordinate formula

For a point \((x,y)\) on the unit circle at an angle \(\theta\), \(x = \cos\theta\) and \(y=\sin\theta\).

Step2: Calculate \(x\) - coordinate

Given \(\theta=- 180^{\circ}\), \(x = \cos(-180^{\circ})\). Since \(\cos(-\alpha)=\cos\alpha\), then \(x=\cos(180^{\circ})=-1\).

Step3: Calculate \(y\) - coordinate

Given \(\theta = - 180^{\circ}\), \(y=\sin(-180^{\circ})\). Since \(\sin(-\alpha)=-\sin\alpha\), then \(y =-\sin(180^{\circ}) = 0\).

Answer:

\((-1,0)\)