Question

enter the coordinates of the point on the unit circle at the given angle. 270° (?, )

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 the \(x\) - coordinate

Given \(\theta = 270^{\circ}\), \(x=\cos(270^{\circ})\). Since \(\cos(270^{\circ})=\cos(360^{\circ}- 90^{\circ})=\cos(90^{\circ}) = 0\).

Step3: Calculate the \(y\) - coordinate

\(y = \sin(270^{\circ})\). Since \(\sin(270^{\circ})=\sin(360^{\circ}-90^{\circ})=-\sin(90^{\circ})=- 1\).

Answer:

\((0,-1)\)