Question

enter the coordinates of the point on the unit circle at the given angle.
-315°
(\frac{\sqrt{?}}{2},\frac{\sqrt{2}}{})

Explanation:

Step1: Find the reference angle

The angle \(-315^{\circ}\) is equivalent to \(45^{\circ}\) (since \(-315^{\circ}+360^{\circ} = 45^{\circ}\)).

Step2: Determine the coordinates

For a unit circle, the coordinates of a point at angle \(\theta\) are \((\cos\theta,\sin\theta)\). For \(\theta = 45^{\circ}\), \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\) and \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\).

Answer:

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