Question

enter the coordinates of the point on the unit circle at the given angle. 300° (\frac{1}{?}, -\frac{\sqrt{}}{2})

Explanation:

Step1: Find the reference angle

The reference angle for \(300^{\circ}\) is \(360^{\circ}-300^{\circ} = 60^{\circ}\)

Step2: Determine the coordinates on the unit circle

For a unit circle, the coordinates of a point at an angle \(\theta\) are \((\cos\theta,\sin\theta)\).
For \(\theta = 300^{\circ}\), \(\cos300^{\circ}=\cos(360^{\circ} - 60^{\circ})=\cos60^{\circ}=\frac{1}{2}\)
\(\sin300^{\circ}=\sin(360^{\circ}-60^{\circ})=-\sin60^{\circ}=-\frac{\sqrt{3}}{2}\)

Answer:

\((\frac{1}{2},-\frac{\sqrt{3}}{2})\)
So the number in the green box is \(2\) and the number in the grey box is \(3\)