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Trigonometric Functions of General Angles

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18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 2 – Find the values of trigonometric functions for general angles. – The definition of a reference angle. – The signs of trigonometric functions in different quadrants. What You Will Learn:

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Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 3 Trigonometric Representation of a General Angle x-axis y-axis x y r (x, y) is in the Standard Position

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Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 4 x y (5, –12) r 5 –12 What are the six trig functions for this angle ? What is r?

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Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 5 x y (5, –12) 13 5 –12 What are the six trig functions for this angle ?

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Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 6 Definition - Given an angle in Standard Position the Reference Angle is the angle formed by the terminal side and the x-axis. It is generally labeled as . x-axis y-axis x-axis y-axis x-axis y-axis x-axis y-axis

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Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 7 x y Quadrant I Direction of a Positive Angle in Standard Position sine + cosine + tangent + What is the upper right corner of the Cartesian Coordinate System labeled as? What is the sign of the sine, cosine, and tangent functions in this quadrant?

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Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 8 x y Quadrant II sine + cosine – tangent – What is the upper left corner of the Cartesian Coordinate System labeled as? What is the sign of the sine, cosine, and tangent functions in this quadrant? Direction of a Negative Angle in Standard Position

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Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 9 x y Quadrant III sine – cosine – tangent + What is the lower left corner of the Cartesian Coordinate System labeled as? What is the sign of the sine, cosine, and tangent functions in this quadrant?

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Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 10 x y Quadrant IV sine – cosine + tangent – What is the lower right corner of the Cartesian Coordinate System labeled as? What is the sign of the sine, cosine, and tangent functions in this quadrant?

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Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 11 x y x y x y x y Quadrant IIQuadrant I Quadrant IIIQuadrant IV Direction of a Positive Angle in Standard Position sine + cosine + tangent + sine + cosine – tangent – sine – cosine – tangent + sine – cosine + tangent – Direction of a Negative Angle in Standard Position Note that each trigonometric function is positive in two quadrants and negative in two quadrants. Is there any pattern to the sign values?

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Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 12 – How to determine the values of trigonometric functions for general angles. – The definition of a reference angle and its relationship to the original angle. – How to determine the signs of trigonometric functions in different quadrants. What You Have Learned:

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Trigonometric Functions of General Angles 18 April 2015Alg2_13_03_GeneralAngleMeasure.ppt Copyrighted © by T. Darrel Westbrook 13 OFLINEEND

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