Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. 2.1 Angles in the Cartesian Plane JMerrill, 2009.

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Presentation transcript:

Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. 2.1 Angles in the Cartesian Plane JMerrill, 2009

Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Angles in Standard Position 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. Cartesian Grid Quadrant II Quadrant I Quadrant III Quadrant IV 90 o 180 o 270 o 360 o 0o0o

Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Sketching Angles in Standard Positions 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 -150 o ?

Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Coterminal angles 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. Your Turn: Measuring of Coterminal Angles  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. Find an angle that is coterminal with:

Trigonometry by Cynthia Y. Young, © 2007 John Wiley and Sons. All rights reserved. Common Angles in Standard Position The common angles with their exact values for their Cartesian coordinates are shown on this graph.