Understanding Reference Angles in Radians

The video tutorial explains how to find reference angles for given angles in radians. It defines a reference angle as the acute angle formed by the terminal side of an angle in standard position with the x-axis. Three examples are provided: 28/25 pi radians, -18/13 radians, and -10/35 pi radians. Each example demonstrates the process of determining the reference angle, including converting improper fractions, using decimal approximations, and considering the direction of rotation. The tutorial emphasizes understanding the relationship between the terminal side and the x-axis to identify the reference angle.

What is a reference angle?

• An angle that is always greater than 90 degrees

• An acute angle formed with the y-axis

• An acute angle formed with the x-axis

• An angle that is always less than 45 degrees

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How can 28/25 pi radians be simplified for easier calculation?

• As 30/25 pi plus 2/25 pi

• As 24/25 pi plus 4/25 pi

• As 25/25 pi plus 3/25 pi

• As 28/28 pi plus 0/25 pi

What is the reference angle for 28/25 pi radians?

• 3/25 pi radians

• 5/25 pi radians

• 7/25 pi radians

• 9/25 pi radians

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What is the approximate decimal value of negative 18/13 radians?

• -1.58

• -1.48

• -1.28

• -1.38

In which range does negative 18/13 radians fall when graphed?

• Between pi/2 and pi radians

• Between pi/6 and pi/4 radians

• Between pi/3 and pi/2 radians

• Between pi/4 and pi/3 radians

What is the reference angle for negative 18/13 radians?

• 16/13 radians

• 18/13 radians

• 14/13 radians

• 12/13 radians

How does the fraction negative 10/35 simplify?

• Negative 3/7

• Negative 2/7

• Negative 1/7

• Negative 4/7

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What is the approximate decimal value of negative 2/7 pi?

• -0.70

• -0.80

• -1.00

• -0.90

In which range does negative 2/7 pi radians fall when graphed?

• Between pi/3 and pi/2 radians

• Between pi/4 and pi/3 radians

• Between pi/6 and pi/4 radians

• Between pi/2 and pi radians

What is the reference angle for negative 2/7 pi radians?

• 2/7 pi radians

• 3/7 pi radians

• 5/7 pi radians

• 4/7 pi radians