Answer:
On a unit circle, the point that corresponds to an angle of [tex]0^{\circ}[/tex] is at position [tex](1, \, 0)[/tex].
The point that corresponds to an angle of [tex]90^{\circ}[/tex] is at position [tex](0, \, 1)[/tex].
Step-by-step explanation:
On a cartesian plane, a unit circle is
- a circle of radius [tex]1[/tex],
- centered at the origin [tex](0, \, 0)[/tex].
The circle crosses the x- and y-axis at four points:
- [tex](1, \, 0)[/tex],
- [tex](0, \, 1)[/tex],
- [tex](-1,\, 0)[/tex], and
- [tex](0,\, -1)[/tex].
Join a point on the circle with the origin using a segment. The "angle" here likely refers to the counter-clockwise angle between the positive x-axis and that segment.
When the angle is equal to [tex]0^\circ[/tex], the segment overlaps with the positive x-axis. The point is on both the circle and the positive x-axis. Its coordinates would be [tex](1, \, 0)[/tex].
To locate the point with a [tex]90^{\circ}[/tex] angle, rotate the [tex]0^\circ[/tex] segment counter-clockwise by [tex]90^{\circ}[/tex]. The segment would land on the positive y-axis. In other words, the [tex]90^{\circ}[/tex]-point would be at the intersection of the positive y-axis and the circle. Its coordinates would be [tex](0, \, 1)[/tex].
