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Example Questions
Example Question #1 : Unit Circle And Radians
What point corresponds to the angle on the unit circle?
The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system.
is equivalent to
which corresponds to the point
on the unit circle.
Example Question #2 : Unit Circle
What point corresponds to an angle of radians on the unit circle?
The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system.
radians is equivalent to
. This is a full circle
plus a quarter-turn
more. So, the angle
corresponds to the point
on the unit circle.
Example Question #1 : Unit Circle
Give the angle between and
that corresponds to the point
.
The angle or
corresponds to the point
.
Example Question #1 : Unit Circle
What point corresponds to the angle on the unit circle?
The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system.
is equivalent to
which corresponds to the point
on the unit circle.
Example Question #2 : Unit Circle
Which of the following points is NOT on the unit circle?
For a point to be on the unit circle, it has to have a radius of one. Therefore, the sum of the squares of point's coordinates must also equal one.
Let's try the point .
Therefore, this point is not on the unit circle.
Example Question #3 : Unit Circle
When looking at the unit circle, what are the coordinates for an angle of ?
The coordinates of the point on the circle for each angle are .
Since and
, the point will be
.
Example Question #1 : Unit Circle
What is the radius of the unit circle?
By definition, the radius of the unit circle is 1.
Example Question #1 : Unit Circle
What point corresponds to the angle on the unit circle?
In order to find the point corresponds to the angle on the unit circle we can write:
In the unit circle which has the radious of we can write:
So the point corresponds to the angle on the unit circle is
Example Question #1 : Unit Circle
What point corresponds to an angle of on the unit circle?
The unit circle is the circle of radius one centered at the origin in the Cartesian coordinate system.
is a full circle
plus a
more. So, the angle
corresponds to the point
on the unit circle.
Example Question #1 : Unit Circle
What must be the area of the unit circle?
The area can vary.
The unit circle must have a radius of 1.
Use the circular area formula to find the area.
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