Trigonometry : Unit Circle

Study concepts, example questions & explanations for Trigonometry

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Example Questions

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Example Question #1 : Unit Circle And Radians

What point corresponds to the angle on the unit circle?

12

Possible Answers:

Correct answer:

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?

12

Possible Answers:

Correct answer:

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 #2 : Unit Circle

Give the angle between  and that corresponds to the point .

Possible Answers:

Correct answer:

Explanation:

The angle  or  corresponds to the point .

Example Question #4 : Unit Circle And Radians

What point corresponds to the angle  on the unit circle?

 

12

 

Possible Answers:

Correct answer:

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 #3 : Unit Circle

Which of the following points is NOT on the unit circle?

Possible Answers:

Correct answer:

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 And Radians

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

Possible Answers:

Correct answer:

Explanation:

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

Since  and , the point will be .

Example Question #4 : Unit Circle

What is the radius of the unit circle? 

Possible Answers:

Correct answer:

Explanation:

By definition, the radius of the unit circle is 1. 

Example Question #8 : Unit Circle And Radians

What point corresponds to the angle  on the unit circle?

 

8

Possible Answers:

Correct answer:

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 #5 : Unit Circle

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

12

Possible Answers:

Correct answer:

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 #6 : Unit Circle

What must be the area of the unit circle?

Possible Answers:

The area can vary.

Correct answer:

Explanation:

The unit circle must have a radius of 1.

Use the circular area formula to find the area.

 

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