Question

enter the coordinates of the point on the unit circle at the given angle. 150° (-\frac{\sqrt{?}}{2}, \frac{1}{})

Explanation:

Step1: Recall unit - circle coordinates

For a point \((x,y)\) on the unit circle at angle \(\theta\), \(x = \cos\theta\) and \(y=\sin\theta\). Here \(\theta = 150^{\circ}\).

Step2: Calculate \(\cos150^{\circ}\)

\(\cos150^{\circ}=\cos(180^{\circ} - 30^{\circ})=-\cos30^{\circ}=-\frac{\sqrt{3}}{2}\).

Step3: Calculate \(\sin150^{\circ}\)

\(\sin150^{\circ}=\sin(180^{\circ}-30^{\circ})=\sin30^{\circ}=\frac{1}{2}\).

Answer:

The number in the green box is \(3\), and the number in the gray box is \(2\).