Radian and Degree Measure

1. Radian and Degree Measure Objectives: Describe Angles Use Radian and Degree measures

2. Trigonometry: the measurement of trianglesthe relationships among the sides and angles of triangles An angle is determined by rotating a ray about its endpoint. The starting position of the ray is the initial sideof the angle and the position after rotation is the terminal side. The endpoint of the ray is the vertexof the angle. This perception of an angle fits a coordinate system in which the origin is the vertex and the initial side coincides with the positive x-axis. Such an angle is in standard position. Counterclockwise rotation generates positive anglesand clockwise rotation generates negative angles. Angle that have the same initial and terminal sides are called coterminal angles.

3. Measure of an angle: the amount of rotation from the initial side to the terminal side. Radian: the measure of a central angle that intercepts an arc equal in length to the radius of the circle. Algebraically, this means that where is measured in radians. (Note that ) Degree: a measure of one degree is equivalent to a rotation of of a complete revolution about the vertex.

4. Conversions between Degrees and Radians • To convert degrees to radians, multiply degrees by EX: Convert from degrees to radians a) b) • To convert radians to degrees, multiply radians by EX: Convert from radians to degrees a) b)

5. Decimal degrees are used to denote fractional parts of degrees Fractional parts of degrees are expressed in minutes and seconds, using the prime and double prime notations, respectively. Many calculators have special keys for converting an angle in degrees, minutes, and seconds to decimal degree form, and vice versa.

6. EXAMPLE A) Determine the quadrant in which the angle lies B) Convert to degrees C) Determine two coterminal angles (one positive and one negative) for each angle. D) Determine the complement and the supplement of each angle (IF POSSIBLE). 1.

7. EXAMPLE A) Determine the quadrant in which the angle lies B) Convert to radians C) Determine two coterminal angles (one positive and one negative) for each angle. D) Determine the complement and the supplement of each angle(IF POSSIBLE). 2.

8. EXAMPLE A) Determine the quadrant in which the angle lies B) Convert to degrees C) Determine two coterminal angles (one positive and one negative) for each angle. 3.

9. EXAMPLE A) Determine the quadrant in which the angle lies B) Convert to radians C) Determine two coterminal angles (one positive and one negative) for each angle. 4.

10. EX 5: Convert to Decimal Degrees. Round to the nearest thousandth of a degree. a) b) c)

11. EX 6: Convert to Degree, Minutes and Seconds a) b) c)