1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Find coterminal and reference angles. Find the trigonometric function values of angles in standard position. 13.2 Angles of Rotation

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms angle of rotation coterminal angle degree initial side negative measure positive measure reference angle standard position terminal side 13.2 Angles of Rotation

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Trigonometric Functions of  13.2 Angles of Rotation r =  x 2 + y 2 sin  = y r cos  = x r tan  = y x, x  0

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Trigonometric Functions of  13.2 Angles of Rotation r =  x 2 + y 2 csc  = r y sec  = r x cot  = x y, y  0, x  0

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Find coterminal angles and reference angles. 13.2 Angles of Rotation Coterminal angles of 217º such that –360º <  < 360º are found as follows: 17º – 360º = –143º Because a 217º angle is in Quadrant III, so the reference angle is |180º – 217º| = 37º.

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Find the trigonometric function values of angles in standard position. 13.2 Angles of Rotation terminal side in Q IV tan  = – 5 4

7. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Find the trigonometric function values of angles in standard position. 13.2 Angles of Rotation Use the Pythagorean Theorem to find r:  4 2 + (–5) 2 =  41 sin  = – 5  41 cos  = 4  41 5  41 41 = 4  41 41 = TOC