1. Objectives Change from radian to degree measure, and vice versa Find angles that are co-terminal with a given angle Find the reference angle for a given angle

2. Angles and Their Measures Angles are formed by the rotation of two rays that share a common and fixed endpoint. If one ray remains fixed, it forms the initial side. The second ray rotates to form the terminal side. If the rotation is in a counter-clockwise direction, it forms a positive angle. If the rotation is in a clockwise direction, it forms a negative angle. An angle that has its vertex at the origin and its initial side along the x-axis, the angle is said to be in standard position.

3. The angles below are all in standard position Positive angle Initial side Terminal side Negative angle Initial side Terminal side Quadrantal Angle Initial Side Terminal Side

4. Angle Measurement There are two common units used to measure angles, degrees and radians. An angle is 1° if it is 1/360 of a revolution in the positive direction. Each degree consists of 60 minutes – 60’. Each minute consists of 60 seconds – 60”.

5. Change 29°45’26” to a decimal number of degrees to the nearest one thousandth 29° + 45’(1/60) + 26”(1/3600) = 29° +.750° +.007° = 29.757°

6. Radians Another unit of measure is the radian. The definition of a radian is based on the unit circle. A unit circle is a circle with a radius of 1. There is an important relationship between degrees and radians. Since one revolution of a circle is either 360° or 2  radians: 360° = 2  radians 180° =  radians 90° =  /2 radians 45° =  /4 radians

7. Degree/Radian Conversion Formulas To change degrees to radians: multiply by  /180 radians To change radians to degrees: multiply by 180°/  1 radian = about 57.3° 1 degree = about 1.017 radians

8. Assignment Make a unit circle with multiples of 30° –Label both degree and radian measures Make a unit circle with multiples of 45° -- label both degree and radian measures Tomorrow - co-terminal angles and reference angles