Understanding Angles and Radians

The video tutorial explains how to plot angles in standard position and convert them from degrees to exact radian measure. It covers three examples: 254 degrees, 123 degrees, and 371 degrees. For each example, the video demonstrates plotting the angle, converting it to radians using the formula (angle in degrees) * (π/180), and simplifying the result. The tutorial also shows how to verify the conversion using a calculator and provides decimal approximations for the radian measures.

What is the initial side of an angle in standard position?

• Along the negative x-axis

• Along the positive y-axis

• Along the positive x-axis

• Along the negative y-axis

How many degrees is one-fourth of a rotation counterclockwise?

• 45 degrees

• 270 degrees

• 180 degrees

• 90 degrees

What is the exact radian measure of 254 degrees?

• 90π/127 radians

• 180π/254 radians

• 254π/180 radians

• 127π/90 radians

Which tool is used to verify the fraction part of the angle in radians?

• Desmos scientific calculator

• Ruler

• Graphing paper

• Protractor

What is the decimal approximation of 127π/90 radians?

• 4.433 radians

• 3.142 radians

• 5.678 radians

• 2.718 radians

What is the common factor between 123 and 180?

• 2

• 6

• 3

• 5

What is the exact radian measure of 123 degrees?

• 180π/123 radians

• 41π/60 radians

• 123π/180 radians

• 60π/41 radians

What is the decimal approximation of 41π/60 radians?

• 4.433 radians

• 3.142 radians

• 2.147 radians

• 1.570 radians

What is the exact radian measure of 371 degrees?

• 371π/360 radians

• 360π/371 radians

• 180π/371 radians

• 371π/180 radians

What is the decimal approximation of 371π/180 radians?

• 8.123 radians

• 6.475 radians

• 5.678 radians

• 7.854 radians