Understanding Reference Angles

The video tutorial explains how to determine reference angles for given angles. It covers the concept of reference angles, which are acute angles formed by the terminal side of a given angle and the x-axis. The tutorial provides three examples: 221 degrees, 347 degrees, and -125 degrees, demonstrating how to calculate the reference angle for each. Reference angles are important for constructing reference triangles and determining trigonometric function values.

What is a reference angle?

• An angle that is always 90 degrees.

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

• An angle that is always less than 45 degrees.

• The angle formed by the initial side and the terminal side of a given angle.

How do you sketch an angle in standard position?

• By rotating the angle clockwise from the x-axis.

• By drawing the angle starting from the y-axis.

• By placing the initial side on the x-axis and rotating counterclockwise.

• By drawing the angle starting from the origin.

What is the reference angle for a 221-degree angle?

• 139 degrees

• 221 degrees

• 41 degrees

• 59 degrees

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CCSS.8.G.A.5

Why are reference angles important?

• They are used to find the area of a triangle.

• They help in determining the length of the hypotenuse.

• They allow us to use special reference triangles to find trigonometric values.

• They are used to measure the height of a triangle.

What is the reference angle for a 347-degree angle?

• 23 degrees

• 47 degrees

• 77 degrees

• 13 degrees

How do you find the reference angle for an angle greater than 180 degrees?

• Subtract the angle from 360 degrees.

• Divide the angle by 2.

• Subtract 180 degrees from the angle.

• Add 180 degrees to the angle.

What is the reference angle for a -125-degree angle?

• 55 degrees

• 125 degrees

• 35 degrees

• 90 degrees

How do you find the reference angle for a negative angle?

• Add 360 degrees to the angle.

• Take the absolute value of the angle.

• Add 180 degrees to the angle.

• Subtract the angle from 180 degrees.

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CCSS.5.G.A.1

What is the significance of sketching a perpendicular from the x-axis to the terminal side?

• It helps in finding the length of the terminal side.

• It is used to construct the reference triangle.

• It determines the initial side of the angle.

• It measures the angle of rotation.

What is the reference angle if the terminal side is 35 degrees past the -y axis?

• 145 degrees

• 125 degrees

• 55 degrees

• 35 degrees