### All Trigonometry Resources

## Example Questions

### Example Question #1 : Unit Circle

What point corresponds to the angle on the unit circle?

**Possible Answers:**

**Correct answer:**

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 And Radians

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

**Possible Answers:**

**Correct answer:**

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 And Radians

Give the angle between and that corresponds to the point .

**Possible Answers:**

**Correct answer:**

The angle or corresponds to the point .

### Example Question #2 : Unit Circle And Radians

What point corresponds to the angle on the unit circle?

**Possible Answers:**

**Correct answer:**

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 And Radians

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

**Possible Answers:**

**Correct answer:**

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 #1 : Unit Circle And Radians

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

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 And Radians

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

**Possible Answers:**

**Correct answer:**

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 #2 : Unit Circle And Radians

What must be the area of the unit circle?

**Possible Answers:**

The area can vary.

**Correct answer:**

The unit circle must have a radius of 1.

Use the circular area formula to find the area.