Trigonometric Functions of General Angles Trigonometric Functions of
- Slides: 13
Trigonometric Functions of General Angles
Trigonometric Functions of General Angles What You Will Learn: – Find the values of trigonometric functions for general angles. – The definition of a reference angle. – The signs of trigonometric functions in different quadrants. 24 September 2021 Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook 2
Trigonometric Functions of General Angles Trigonometric Representation of a General Angle y-axis (x, y) y r x 24 September 2021 is in the Standard Position x-axis Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook 3
Trigonometric Functions of General Angles What are the six trig functions for this angle ? What is r? y 5 x – 12 r (5, – 12) 24 September 2021 Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook 4
Trigonometric Functions of General Angles What are the six trig functions for this angle ? y 5 13 x – 12 (5, – 12) 24 September 2021 Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook 5
Trigonometric Functions of General Angles 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 . y-axis x-axis y-axis 24 September 2021 y-axis x-axis Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook x-axis 6
Trigonometric Functions of General Angles y Whatisisthe theupper sign What of thecorner sine, cosine, right of the and tangent Cartesian functions in this Coordinate quadrant? System labeled as? 24 September 2021 Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook Quadrant I sine + cosine + tangent + Direction of a Positive Angle in Standard Position x 7
Trigonometric Functions of General Angles Quadrant II sine + cosine – y tangent – x Direction of a Negative Angle in Standard Position 24 September 2021 Whatisisthe theupper sign What ofleft thecorner sine, cosine, of the and tangent Cartesian functions in this Coordinate quadrant? System labeled as? Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook 8
Trigonometric Functions of General Angles y Quadrant III sine – cosine – Whatisisthe thelower sign What ofleft thecorner sine, cosine, of the and tangent Cartesian functions in this Coordinate quadrant? System labeled as? x tangent + 24 September 2021 Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook 9
Trigonometric Functions of General Angles Whatisisthe thelower sign What of thecorner sine, cosine, right of the and tangent Cartesian functions in this Coordinate quadrant? System labeled as? y Quadrant IV sine – cosine + x tangent – 24 September 2021 Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook 10
Trigonometric Functions of General Angles Quadrant II sine + cosine – y y tangent – x Direction of a Negative Angle in Standard Position Note that each trigonometric function is positive in two quadrants and negative in two y quadrants. Is there any pattern to the sign values? Quadrant III sine – cosine – sine + cosine + tangent + Direction of a Positive Angle in Standard Position x y Quadrant IV x tangent + 24 September 2021 Quadrant I sine – cosine + x tangent – Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook 11
Trigonometric Functions of General Angles What You Have Learned: – 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. 24 September 2021 Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook 12
Trigonometric Functions of General Angles END OF LINE 24 September 2021 Alg 2_13_03_General. Angle. Measure. ppt Copyrighted © by T. Darrel Westbrook 13
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