Angles and Their Measure

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Presentation transcript:

Angles and Their Measure Objective: Students will be able to find coterminal and reference angles. Students will also be able to find the arc length and area of a sector. EQ: How do I measure angles and put them in standard position? What are radians and how do they relate to degrees and trigonometry in general? Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Standard position: Vertex is at the origin Copyright © 2013 Pearson Education, Inc. All rights reserved

Finding Coterminal Angles Two angles with the same initial and terminal sides but possibly different rotations are called coterminal angles. Smallest angle made from the terminal side to x-axis is called the reference angle. It is always positive and < 90˚. Assume the following angles are in standard position. Coterminal and/or reference angle: a. 400° angle b. –135° angle

Copyright © 2013 Pearson Education, Inc. All rights reserved

Convert 40°12’5” to a decimal in degrees Convert 40°12’5” to a decimal in degrees. Round the answer to four decimal places. Convert 78.562° to the D°M’S” form. Round the answer to the nearest second. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Definition of a Radian One radian is the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle.

Copyright © 2013 Pearson Education, Inc. All rights reserved

360° Copyright © 2013 Pearson Education, Inc. All rights reserved

(a) 30° (b) 120° (c) – 60° (d) 270° (e) 104 ° Copyright © 2013 Pearson Education, Inc. All rights reserved

Draw and label the angle in standard position. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 0.5 radian. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Find the area of the sector of a circle of radius 5 feet formed by an angle of 60˚. Round the answer to two decimal places. Copyright © 2013 Pearson Education, Inc. All rights reserved