Understanding Radian Measure

This video tutorial introduces radian measure, explaining its basis on the circle's radius. It covers conversions between degrees and radians, using equations and visual demonstrations. Key angles and their radian measures are highlighted, along with methods to find trigonometric function values in radians. The video emphasizes understanding the natural unit of radians and its application in trigonometry.

What is the basis of a radian as a unit of measure?

• The diameter of a circle

• The radius of a circle

• The circumference of a circle

• An arbitrary division of a circle

How many degrees are equivalent to 2π radians?

• 180 degrees

• 90 degrees

• 360 degrees

• 270 degrees

What is the radian measure of a 30-degree angle?

• π/2 radians

• π/3 radians

• π/4 radians

• π/6 radians

If 90 degrees is 1/4 of a revolution, what is its radian measure?

• π/2 radians

• π/3 radians

• π radians

• π/4 radians

What is the conversion factor from degrees to radians?

• 90/π

• 180/π

• π/180

• π/90

What is the degree measure of π/2 radians?

• 30 degrees

• 60 degrees

• 90 degrees

• 45 degrees

Which angle in degrees is equivalent to π/4 radians?

• 60 degrees

• 90 degrees

• 30 degrees

• 45 degrees

What is the tangent of 120 degrees?

• √3

• -√3

• -1

• 1

What is the sine of 270 degrees?

• -1

• √3/2

• 0

• 1

Which of the following is a key angle in radian measure?

• 15 degrees = π/12

• 30 degrees = π/6

• 45 degrees = π/5

• 60 degrees = π/5