Question

Type the correct answer in the box. Use a comma to separate the x- and y-coordinates of each point. The coordinates of the point on the unit circle that corresponds to an angle of 0º are ( ). The coordinates of the point on the unit circle that corresponds to an angle of 90º are ( ).

Answer 1

Answer:

On a unit circle, the point that corresponds to an angle of $0^{\circ}$ is at position $(1, \, 0)$.

The point that corresponds to an angle of $90^{\circ}$ is at position $(0, \, 1)$.

Step-by-step explanation:

On a cartesian plane, a unit circle is

• a circle of radius $1$,
• centered at the origin $(0, \, 0)$.

The circle crosses the x- and y-axis at four points:

• $(1, \, 0)$,
• $(0, \, 1)$,
• $(-1,\, 0)$, and
• $(0,\, -1)$.

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 $0^\circ$, the segment overlaps with the positive x-axis. The point is on both the circle and the positive x-axis. Its coordinates would be $(1, \, 0)$.

To locate the point with a $90^{\circ}$ angle, rotate the $0^\circ$ segment counter-clockwise by $90^{\circ}$. The segment would land on the positive y-axis. In other words, the $90^{\circ}$-point would be at the intersection of the positive y-axis and the circle. Its coordinates would be $(0, \, 1)$.