Angles in Degree & Radian Measure w/Unit Circle

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Presentation transcript:

Angles in Degree & Radian Measure w/Unit Circle Unit 6 Trig Angles in Degree & Radian Measure w/Unit Circle

Angle Measure Standard Position: an angle in the coordinate plane with vertex at the origin and one ray(side) on the positive x-axis. Initial side: the ray on the x-axis Terminal side: the other side of the angle. y x Angle Measure o

Unit circle 900 ? 1200 600 ANGLE MEASURE ? 450 ? 1350 300 1500 3600 1800 00 ? ? 2100 3300 2250 ? 3150 ? 2400 3000 2700 ?

0o & 3600 are Coterminal angles b/c they have the same terminal side Degree measure What is a angle that is coterminal with -225o? 0o & 3600 are Coterminal angles b/c they have the same terminal side How many degrees in a circle? (One full revolution) 90o y x y x 135o ? 180o 360o 270o 0o Is 495o coterminal with the above angles? The measure is negative when the rotation is clockwise.

White board practice 315o ? 45o ? -150o ? -315o 405o 210o -510o -45o Sketch each angle, can you find another that is coterminal? -315o 405o 315o ? 45o ? -150o ? 45o y x -150o 315o 210o -510o -45o 675o

Radian Measures Radian is a another unit of measure for angles (in terms of pi) To convert Degree measure to Radians multiply by To convert Radians measure to Degree multiply by Convert to radian measure Convert to degree measure y x 150o -60o 150o -60o

Unit circle 900 ? 1200 600 ANGLE MEASURE RADIANS 450 ? 1350 300 1500 1800 360o ? 2100 3300 2250 ? 3150 ? 2400 3000 2700 ?

Draw an angle with the given measure. It might help to convert to degrees Look at unit circle: can you find it?

Answer: 350o

Answer:

Practice angle measure: pg 832 #13-25 Radians pg 840 #7-15 odd, 26-33

Homework Workbook pg 343 #4-11 Work book pg 347 #1-11, 21-26