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 © 2017 E. Choi – MHF4U - All Rights Reserved

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

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

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

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

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

Example 1: a) 2 -4 -1 3 -3 𝜋 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) 2 -4 -1 3 -3 𝜋 𝜋/2 -𝜋/8 7𝜋/8 3𝜋/8 Trigonometric Graphs Transformation © 2017 E. Choi – MHF4U - All Rights Reserved

Example 1: State the amplitude and period of each trigonometric function, then sketch the graph. b) 2.5 1.5 2 0.5 -0.5 4𝜋 2𝜋 2𝜋 6𝜋 4𝜋 Trigonometric Graphs Transformation © 2017 E. Choi – MHF4U - All Rights Reserved

Example 2: Trigonometric Graphs Transformation © 2017 E. Choi – MHF4U - All Rights Reserved

Example 3: Converting Between Sine and Cosine Convert the following from sine to cosine or vice versa. Trigonometric Graphs Transformation © 2017 E. Choi – MHF4U - All Rights Reserved

Example 3: Converting Between Sine and Cosine Convert the following from sine to cosine or vice versa. Trigonometric Graphs Transformation © 2017 E. Choi – MHF4U - All Rights Reserved

Homework Text Book: P. 267 #4-7,9,10,13,15,18 Work Sheet: WS: Converting between Sine & Cosine Check the website for updates Trigonometric Graphs Transformation © 2017 E. Choi – MHF4U - All Rights Reserved

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