Transcript 2.1
JMerrill, 2009 Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. 2.1 Angles in the Cartesian Plane An angle is said to be in standard position if its initial side is along the positive x-axis and its vertex is at the origin. We say that an angle lies in the quadrant in which its terminal side lies. Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Angles in Standard Position 90o Quadrant II Quadrant I 180o 0o 360o Quadrant III Quadrant IV 270o Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Cartesian Grid Sketching a 210º angle in the standard position yields this graph. •The initial side lies on the x-axis. •The positive angle indicates counterclockwise rotation. •180º represents a straight angle and the additional 30º yields a 210 º angle. •The terminal side lies in quadrant III. •What can you tell me about the angle -150o? Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Sketching Angles in Standard Positions Two angles in standard position with the same terminal side are called coterminal angles. For example, -40º and 320º are coterminal angles. Moving 40º in clockwise direction brings the terminal side to the same position as moving 320º in the counter-clockwise direction. Such angles may also be reached by going the same direction, such as 90º and 450º. 450º is reached by moving counterclockwise through the full 360º circle, then continuing another 90 º. So, you can find coterminal angles by adding or subtracting a whole circle. Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Coterminal angles Find an angle that is coterminal with: 580º Solution: Subtract 360º to find the correct angle of 220º. -400º Solution: Add 360º to get -40º. Add 360º again to get the correct angle of 320º. Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Your Turn: Measuring of Coterminal Angles The common angles with their exact values for their Cartesian coordinates are shown on this graph. Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Common Angles in Standard Position