Reference Angles and Coterminal Angles

The video tutorial covers coterminal and reference angles. It begins with an introduction to coterminal angles, explaining their properties and how to calculate them in both positive and negative forms. The tutorial then moves on to identifying whether two angles are coterminal. Following this, the concept of reference angles is introduced, detailing their properties and how to calculate them in both degrees and radians. The tutorial concludes with practice problems and a reminder to study for the upcoming test.

What is a coterminal angle?

• An angle that has the same initial and terminal sides but different measures.

• An angle that is always positive.

• An angle that is always negative.

• An angle that is exactly 90 degrees.

How do you find a positive coterminal angle for a given angle in degrees?

• Divide the angle by 2.

• Subtract 360 degrees from the given angle.

• Add 360 degrees to the given angle.

• Multiply the angle by 2.

What is the result of subtracting 360 degrees from 74 degrees?

• -434 degrees

• 434 degrees

• 286 degrees

• -286 degrees

Why are there infinite coterminal angles for a given angle?

• Because you can only add 360 degrees once.

• Because angles can only be negative.

• Because you can add or subtract multiples of 360 degrees indefinitely.

• Because angles can only be positive.

How do you find a coterminal angle in radians?

• Add or subtract π/2 from the given angle.

• Add or subtract 2π from the given angle.

• Multiply the angle by π.

• Divide the angle by π.

Are the angles -30 and 330 coterminal?

• No, because they are in different quadrants.

• Yes, because they have the same initial and terminal sides.

• Yes, because they are both positive.

• No, because one is negative and the other is positive.

What is a reference angle?

• An angle that is always positive.

• An angle that measures the distance from the x-axis.

• An angle that is always 90 degrees.

• An angle that is always negative.

Which of the following is NOT a property of a reference angle?

• It must be less than 90 degrees.

• It must be in quadrant one.

• It must be positive.

• It must be negative.

How do you find the reference angle for 132 degrees?

• Add 132 to 180.

• Subtract 132 from 360.

• Subtract 132 from 180.

• Add 132 to 90.

What is the reference angle for 9π/7 radians?

• π/7

• 4π/7

• 2π/7

• 3π/7