6.1 Radian and Degree Measure

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Presentation transcript:

6.1 Radian and Degree Measure Measuring Angles The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. There are two common ways to measure angles, in degrees and in radians. We’ll start with degrees, denoted by the symbol º. One degree (1º) is equivalent to a rotation of of one revolution.

6.1 Radian and Degree Measure Measuring Angles

6.1 Radian and Degree Measure Radian Measure A second way to measure angles is in radians. Definition of Radian: One radian is the measure of a central angle  that intercepts arc s equal in length to the radius r of the circle. In general,

6.1 Radian and Degree Measure Radian Measure

6.1 Radian and Degree Measure Radian Measure

6.1 Radian and Degree Measure Conversions Between Degrees and Radians To convert degrees to radians, multiply degrees by To convert radians to degrees, multiply radians by

Ex 5. Convert the degrees to radian measure. 60 30 -54 -118 45

Ex 6. Convert the radians to degrees. a) b) c) d)

Ex 7. Find one positive and one negative angle that is coterminal with the angle  = in standard position. Ex 8. Find one positive and one negative angle that is coterminal with the angle  = in standard position.

Degree and Radian Form of “Special” Angles 0°  360 °  30 °  45 °  60 °  330 °  315 °  300 °   120 °  135 °  150 °  240 °  225 °  210 °  180 ° 90 °  270 °   Degree and Radian Form of “Special” Angles

Class Work Convert from degrees to radians. 54 -300 Convert from radians to degrees. 3. 4.

Find one postive angle and one negative angle in standard position that are coterminal with the given angle. 135

HW p474 1-29 odd, 37-41odd, 43-47odd