Measurement of Rotation Section 2.2 Measurement of Rotation

An angle is in standard position in a Cartesian coordinate system if Definition: Standard Position of an Angle An angle is in standard position in a Cartesian coordinate system if Its vertex is at the origin Its initial side is along the positive horizontal axis It is measured counterclockwise from the horizontal axis if the angle measure is positive and clockwise from the horizontal axis if the angle measure is negative Note: We will be using a u-v coordinate system instead of x-y

Definition: Coterminal Angles Two angles in standard position are coterminal if and only if their degree measures differ by a multiple of 360 degrees. That is and are coterminal if and only if where n stands for an integer. Note: coterminal angles have terminal sides that coincide, hence the name

Definition: Reference Angle The reference angle of an angle in standard position is the positive, acute angle between the horizontal axis and the terminal side. Note: Reference angles are always measured counterclockwise. Angles whose terminal sides fall on one of the axes do not have reference angles.

1 What is the reference angle measurement for an angle of 71 degrees in standard position?

2 What is the reference angle measurement for an angle of 133 degrees in standard position?

3 What is the reference angle measurement for an angle of 254 degrees in standard position?

4 What is the reference angle measurement for an angle of 317 degrees in standard position?

Example 2 Sketch an angle of 48970 in standard position, and determine a coterminal angle between 0 and 360 degrees.

5 What is the reference angle for an angle of 4897 degrees in standard position?