Copyright © 2011 Pearson, Inc. 4.3 Trigonometry Extended: The Circular Functions.

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Presentation transcript:

Copyright © 2011 Pearson, Inc. 4.3 Trigonometry Extended: The Circular Functions

Copyright © 2011 Pearson, Inc. Slide Initial Side, Terminal Side

Copyright © 2011 Pearson, Inc. Slide Positive Angle, Negative Angle

Copyright © 2011 Pearson, Inc. Slide Coterminal Angles Two angles in an extended angle-measurement system can have the same initial side and the same terminal side, yet have different measures. Such angles are called coterminal angles.

Copyright © 2011 Pearson, Inc. Slide Example Finding Coterminal Angles

Copyright © 2011 Pearson, Inc. Slide Example Finding Coterminal Angles

Copyright © 2011 Pearson, Inc. Slide Example Finding Coterminal Angles

Copyright © 2011 Pearson, Inc. Slide Example Finding Coterminal Angles

Copyright © 2011 Pearson, Inc. Slide Example Evaluating Trig Functions Determined by a Point in QI

Copyright © 2011 Pearson, Inc. Slide Example Evaluating Trig Functions Determined by a Point in QI

Copyright © 2011 Pearson, Inc. Slide Trigonometric Functions of any Angle

Copyright © 2011 Pearson, Inc. Slide Evaluating Trig Functions of a Nonquadrantal Angle θ 1. Draw the angle θ in standard position, being careful to place the terminal side in the correct quadrant. 2. Without declaring a scale on either axis, label a point P (other than the origin) on the terminal side of θ. 3. Draw a perpendicular segment from P to the x-axis, determining the reference triangle. If this triangle is one of the triangles whose ratios you know, label the sides accordingly. If it is not, then you will need to use your calculator.

Copyright © 2011 Pearson, Inc. Slide Evaluating Trig Functions of a Nonquadrantal Angle θ 4.Use the sides of the triangle to determine the coordinates of point P, making them positive or negative according to the signs of x and y in that particular quadrant. 5.Use the coordinates of point P and the definitions to determine the six trig functions.

Copyright © 2011 Pearson, Inc. Slide Example Evaluating More Trig Functions

Copyright © 2011 Pearson, Inc. Slide Example Evaluating More Trig Functions

Copyright © 2011 Pearson, Inc. Slide Example Using one Trig Ration to Find the Others

Copyright © 2011 Pearson, Inc. Slide Example Using one Trig Ration to Find the Others

Copyright © 2011 Pearson, Inc. Slide Example Using one Trig Ration to Find the Others

Copyright © 2011 Pearson, Inc. Slide Unit Circle The unit circle is a circle of radius 1 centered at the origin.

Copyright © 2011 Pearson, Inc. Slide Trigonometric Functions of Real Numbers

Copyright © 2011 Pearson, Inc. Slide Periodic Function

Copyright © 2011 Pearson, Inc. Slide The 16-Point Unit Circle