Understanding Angles and the Unit Circle

The video tutorial introduces the concept of angles in the unit circle, explaining the initial and terminal sides of an angle. It covers the four quadrants of the Cartesian coordinate plane and how angles are placed within these quadrants. The tutorial demonstrates how to rotate angles, both positive and negative, and identifies the resulting quadrant. It also explains quadrantal angles, which lie on the axes, and discusses the standard position of angles. The video concludes with a summary of positive and negative rotations and their respective quadrants.

What is the initial side of an angle in the unit circle?

• The side that remains fixed on the positive x-axis

• The side that rotates

• The side that lies on the y-axis

• The side that is perpendicular to the x-axis

How many quadrants are there in the Cartesian coordinate plane?

• Five

• Two

• Three

• Four

In which quadrant does the angle 7π/4 lie?

• Quadrant 2

• Quadrant 1

• Quadrant 4

• Quadrant 3

What is the effect of a negative angle on rotation direction?

• It rotates clockwise

• It rotates counterclockwise

• It does not rotate

• It rotates in both directions

What is a quadrantal angle?

• An angle that is less than 90 degrees

• An angle that is greater than 360 degrees

• An angle that lies on an axis

• An angle that lies in the first quadrant

What is the standard position of an angle?

• When its vertex is at the origin and the initial side is on the negative x-axis

• When its vertex is at the origin and the initial side is on the y-axis

• When its vertex is at the origin and the initial side is on the negative y-axis

• When its vertex is at the origin and the initial side is on the positive x-axis

How do positive angles rotate in the unit circle?

• Both directions

• Counterclockwise

• Clockwise

• They do not rotate

What is the angle in radians for a full rotation around the unit circle?

• π

• 3π

• 4π

• 2π

Which angle is equivalent to 90 degrees in radians?

• π/2

• π

• 3π/2

• 2π

What happens when an angle ends on an axis?

• It is called a quadrantal angle

• It is called a terminal angle

• It is called a rotational angle

• It is called a bisecting angle