Trigonometric Functions of General Angles Trigonometric Functions of

  • Slides: 13
Download presentation
Trigonometric Functions of General Angles

Trigonometric Functions of General Angles

Trigonometric Functions of General Angles What You Will Learn: – Find the values of

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)

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

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

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

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,

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 –

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

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

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

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

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.

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