Exploring the Unit Circle in PreCalculus

This video tutorial introduces the concept of radians, a unit of angular measure, and explains its relationship with the unit circle. The unit circle, with a radius of one, is used to demonstrate how angles can be measured in radians instead of degrees. The tutorial discusses the circumference of a circle and how it relates to radians, providing a more precise mathematical approach than degrees. It also covers the conversion between radians and degrees, offering practical examples to illustrate the process. The video emphasizes the advantages of using radians in mathematical contexts over the traditional degree system.

What is the radius of the unit circle?

• 0

• 1

• π

• 2

What is the circumference of a unit circle?

• 1

• π

• 2π

• 2

How many radians are there in a full circle?

• 180

• π

• 2π

• 360

What is π radians equivalent to in degrees?

• 270 degrees

• 90 degrees

• 180 degrees

• 360 degrees

How do you convert radians to degrees?

• Divide by 180/π

• Divide by π/180

• Multiply by 180/π

• Multiply by π/180

What is π/2 radians in degrees?

• 180 degrees

• 360 degrees

• 90 degrees

• 45 degrees

How many radians are in 90 degrees?

• 2π

• π/2

• π/4

• π

If an angle measures 2π/3 radians, what is its measure in degrees?

• 120 degrees

• 90 degrees

• 60 degrees

• 180 degrees

What is 150 degrees in radians?

• π/2

• π/3

• 5π/3

• π/6

What is the radian measure of a 330-degree angle?

• π/3

• 5π/6

• π/6

• 11π/6