Grade 12 Advanced Functions (MHF4U) Unit 4: Trigonometry 2 Trigonometric Graphs Transformation 2 Mr. Choi © 2017 E. Choi – MHF4U - All Rights Reserved.

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Grade 12 Advanced Functions (MHF4U) Unit 4: Trigonometry 2 Trigonometric Graphs Transformation 2 Mr. Choi © 2017 E. Choi – MHF4U - All Rights Reserved

Trigonometric Graphs y = sinx & y = cos x Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

Trigonometric Graphs y = tanx Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

Trigonometric Graphs y = cotx Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

Trigonometric Graphs y = cscx Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

Trigonometric Graphs y = secx Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

Trigonometric Graphs y = asinkx & y = acoskx Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

Example 1: a) 4 -2 1 3 -3 2𝜋 For the sinusoidal functions given below i) Draw the function and highlight one cycle of each function. ii) State the amplitude, period, phase shift, and vertical translation of each function. iii) State the domain and range. a) 4 -2 1 3 -3 2𝜋 𝜋 -𝜋 𝜋 Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

Example 1: b) 5 2 3 2𝜋/3 1 -2 For the sinusoidal functions given below i) Draw the function and highlight one cycle of each function. ii) State the amplitude, period, phase shift, and vertical translation of each function. iii) State the domain and range. b) 5 1 3 2 -2 2𝜋/3 𝜋/3 𝜋/4 11𝜋/12 7𝜋/12 Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

Example 2: Write an equation of this sinusoidal function. State the vertical displacement. Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

Example 3: Write an equation to represent a i) Sine function, ii) Cosine function with the following properties. Maximum: 23 Minimum: 11 Period 5 Phase shift: 9 Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

Find an equation of a function of the form Example 4: Find an equation of a function of the form whose graph passes through the point A . Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

Homework Text Book: P. 273 #1- 12 Work Sheet: Check the website for updates Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved

End of lesson Trigonometric Graphs Transformation 2 © 2017 E. Choi – MHF4U - All Rights Reserved