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

Angle of 0º: (1,0)

Angle of 90º: (0,1)

Explanation:

A unit circle has a radius of 1.

Therefore, the points on the x- and y-axis are as follows:

Angle of 0º: (1,0)

Angle of 90º: (0,1)

Angle of 180º: (-1,0)

Angle of 270º: (0,-1)

Angle of 360º [have now circled back to an angle of 0º]: (1,0)

Answer 2

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)`.

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)`.