Understanding Reference Angles

The video tutorial explains how to determine reference angles for negative angles in standard position. It covers the definition of a reference angle and demonstrates the process of sketching angles of -256, -287, and -148 degrees. For each angle, the tutorial shows how to find the reference angle using both geometric reasoning and arithmetic calculations involving absolute values.

What is a reference angle?

• The angle formed by the y-axis and the terminal side

• An angle that is always negative

• The positive acute angle formed by the x-axis and the terminal side of a given angle

• An angle greater than 180 degrees

How do you sketch a negative angle in standard position?

• Rotate clockwise from the negative x-axis

• Rotate counterclockwise from the negative x-axis

• Rotate clockwise from the positive x-axis

• Rotate counterclockwise from the positive x-axis

What is the reference angle for -256 degrees?

• 180 degrees

• 104 degrees

• 76 degrees

• 256 degrees

Which method can be used to find the reference angle for -256 degrees?

• Multiplying the angle by 2

• Dividing the angle by 2

• Subtracting the absolute value of -180 degrees from the absolute value of -256 degrees

• Adding 180 degrees to the angle

What is the reference angle for -287 degrees?

• 287 degrees

• 17 degrees

• 90 degrees

• 73 degrees

How can you determine the reference angle for -287 degrees using a right angle?

• By adding 17 degrees to 90 degrees

• By subtracting 17 degrees from 90 degrees

• By multiplying 17 degrees by 90 degrees

• By dividing 17 degrees by 90 degrees

What is the reference angle for -148 degrees?

• 58 degrees

• 32 degrees

• 90 degrees

• 148 degrees

How can you find the reference angle for -148 degrees using absolute values?

• By adding the absolute value of -180 degrees to the absolute value of -148 degrees

• By multiplying the absolute values of -180 degrees and -148 degrees

• By subtracting the absolute value of -148 degrees from the absolute value of -180 degrees

• By dividing the absolute value of -180 degrees by the absolute value of -148 degrees

What is the significance of the x-axis in determining reference angles?

• It is irrelevant in angle measurement

• It forms the baseline for measuring the positive acute angle

• It is only used for angles less than 90 degrees

• It is used to measure angles greater than 180 degrees

What is the first step in sketching a negative angle?

• Start from the positive y-axis

• Start from the positive x-axis

• Start from the negative x-axis

• Start from the negative y-axis