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Radian and Degree Measure

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1 Radian and Degree Measure
MAT 200 Radian and Degree Measure In this section, we will study the following topics: Vocabulary used to describe angles Degree measure of an angle Radian measure of an angle Converting between radian and degree measure Find coterminal angles

2 Radian and Degree Measure
MAT 200 Radian and Degree Measure Important Vocabulary for this Lesson: Angle Degrees Radians Angle in Standard Position Coterminal angle Reference Angle Initial Arm Terminal Arm

3 Radian and Degree Measure
Angles Trigonometry: measurement of triangles Angle Measure

4 Radian and Degree Measure
Standard Position Reference Angle Vertex at origin The initial side of an angle in standard position is always located on the positive x-axis.

5 Radian and Degree Measure
Positive and negative angles When sketching angles, always use an arrow to show direction.

6 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.

7 Radian and Degree Measure
Measuring Angles

8 Radian and Degree Measure
Classifying Angles Angles are often classified according to the quadrant in which their terminal sides lie. Ex1: Name the quadrant in which each angle lies. 50º 208º II I -75º III IV Quadrant 1 Quadrant 3 Quadrant 4

9 Radian and Degree Measure
Coterminal Angles Angles that have the same initial and terminal sides are coterminal. Angles  and  are coterminal.

10 Radian and Degree Measure
Example of Finding Coterminal Angles You can find an angle that is coterminal to a given angle  by adding or subtracting multiples of 360º. In general, to find coterminal angles, θ = ± 360ºn where n is a positive integer Ex 2: Find one positive and one negative angle that are coterminal to 112º. For a positive coterminal angle, add 360º : 112º + 360º = 472º For a negative coterminal angle, subtract 360º: 112º - 360º = -248º

11 Ex 3. Find one positive and one negative angle that is coterminal with the angle  = 30° in standard position. Ex 4. Find one positive and one negative angle that is coterminal with the angle  = 272 in standard position.

12 STOP! Time to do an activity!

13 Radian and Degree Measure
Radian Measure In the activity you did, the angle AOB that you found has a measure of 1 radian 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,

14 Radian and Degree Measure
Radian Measure

15 Radian and Degree Measure
Radian Measure

16 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

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

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

19 Ex 7. Find one positive and one negative angle that is coterminal with the angle  = in standard position. Hint: for coterminal angles in radians, θ = ± 2πn Ex 8. Find one positive and one negative angle that is coterminal with the angle  = in standard position.

20 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

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

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


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