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

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

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

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

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

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

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

8. 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

9. 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

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

11. 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

12. 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

13. 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

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