enter the coordinates of the point on the unit circle at the given angle. - 45 ^ { circ } ( \frac { sqrt {…

enter the coordinates of the point on the unit circle at the given angle. - 45 ^ { circ } ( \frac { sqrt {? } } { 2 }, - \frac { sqrt { 2 } } { square } )

enter the coordinates of the point on the unit circle at the given angle. - 45 ^ { circ } ( \frac { sqrt {? } } { 2 }, - \frac { sqrt { 2 } } { square } )

Answer

Explanation:

Step1: Recall the unit - circle coordinates formula

For a point ((x,y)) on the unit circle corresponding to an angle (\theta), (x = \cos\theta) and (y=\sin\theta). Given (\theta=- 45^{\circ}), (\cos(-45^{\circ})=\cos(45^{\circ})) (since (\cos(-\alpha)=\cos\alpha)) and (\sin(-45^{\circ})=-\sin(45^{\circ})).

Step2: Calculate (\cos(45^{\circ})) and (\sin(45^{\circ}))

We know that (\cos(45^{\circ})=\frac{\sqrt{2}}{2}) and (\sin(45^{\circ})=\frac{\sqrt{2}}{2}).

Answer:

The number in the green box (under the square - root) is (2), and the number in the gray box is (2). So the coordinates are (\left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right))