# Trigonometry : Unit Circle and Radians

## Example Questions

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### Example Question #1 : Unit Circle

What point corresponds to the angle on the unit circle?

Explanation:

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 #1 : Unit Circle

What point corresponds to an angle of  radians on the unit circle?

Explanation:

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 .

Explanation:

The angle  or  corresponds to the point .

### Example Question #1 : Unit Circle And Radians

What point corresponds to the angle  on the unit circle?

Explanation:

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?

Explanation:

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 #6 : Unit Circle

When looking at the unit circle, what are the coordinates for an angle of ?

Explanation:

The coordinates of the point on the circle for each angle are .

Since  and , the point will be .

### Example Question #1 : Unit Circle And Radians

What is the radius of the unit circle?

Explanation:

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?

Explanation:

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?

Explanation:

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 #3 : Unit Circle

What must be the area of the unit circle?

The area can vary.