Angle and Angle Measure Angles and Angle Measure

Angle and Angle Measure

Angles and Angle Measure What You Will Learn: – To change radian measure to degree and vice versa , and – To identify coterminal angles. 25 -Feb-21 Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook 2

Angles and Angle Measure An angle is in standard position if its vertex is at the origin and its initial side is along the x-axis. ISBN 0 -07 -827999 -2 25 -Feb-21 Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook 3

Angles and Angle Measure ISBN 0 -07 -827999 -2 25 -Feb-21 Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook 4

Angles and Angle Measure Different angles can have the same coterminal side. The angles are called coterminal angles. ISBN 0 -07 -827999 -2 25 -Feb-21 Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook 5

Angles and Angle Measure 2 radian 3 radian What is a radian? 1 radian arc radius And a little bit more 4 radian 6 radian 5 radian 25 -Feb-21 Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook 6

Angles and Angle Measure There are some angles that are used often, due to their ease of use and everyone’s familiarity with those angles. They are generally arranged in a table or graphic form. It is called a Unit Circle. Why Unit Circle? 25 -Feb-21 Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook 7

Angles and Angle Measure Radius = 1 unit ISBN 0 -07 -827999 -2 25 -Feb-21 Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook 8

Angles and Angle Measure 0 6 4 3 2 2 3 3 4 5 6 7 6 5 4 4 3 3 2 5 3 7 4 11 6 2 0 o 30 o 45 o 60 o 90 o 120 o 135 o 150 o 180 o 210 o 225 o 240 o 270 o 300 o 315 o 330 o 360 o sin 0 1 2 2 2 3 2 1 3 2 2 2 1 2 0 – cos 1 3 2 2 2 1 2 0 – 3 2 – 2 2 – 1 – tan 0 3 3 1 3 und – 3 – 1 3 3 0 3 3 1 csc und 2 2 2 3 3 1 2 3 3 2 2 und – 2 sec 1 2 3 3 2 2 und – 2 2 3 3 – 1 2 3 3 cot und 3 1 3 3 0 3 25 -Feb-21 – 1 2 3 3 – – 1 – – – 3 und – 2 2 – 3 2 – 1 3 2 – 2 2 – 1 2 0 1 2 2 2 3 und – 3 – 1 2 3 3 – 1 – – 2 und 1 3 3 0 1 2 – Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook – 3 2 – 2 2 – 1 2 0 3 2 1 – – 3 3 0 2 3 2 – 2 und 2 2 2 3 3 1 3 3 – 1 – 3 und – 9

Angles and Angle Measure All circles are similar. They all have 360 o inside. This 360 o equates to 2 radians per circle. 360 o 180 o = =1 2 radians 60 o to radians 60 o 1 radians o 60 180 o radians 3 25 -Feb-21 7 radians 3 180 o radians 420 o Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook 10

Angles and Angle Measure Definition: Coterminal – When two angles in standard position have the same terminal side. 25 -Feb-21 Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook 11

Angles and Angle Measure What You Have Learned: – To change radian measure to degree and vice versa , and – To identify coterminal angles. 25 -Feb-21 Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook 12

Angles and Angle Measure END OF LINE 25 -Feb-21 Alg 2_13_02_Angle. And. Angle. Measurement. ppt Copyrighted © by T. Darrel Westbrook 13