1. Trigonometric Functions of General Angles

2. 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:

3. 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

4. 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?

5. 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  ?

6. 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 

7. 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?

8. 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

9. 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?

10. 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?

11. 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?

12. 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:

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