Advanced Trigonometry - Trigonometric functions and graphing

This lesson comprises four (4) master classes focusing on:

• Trigonometric functions
• Trigonometric equations
• Function transformations
• Sketching functions

Content:

MA-T3

• Examine and apply transformations to sketch functions of the form \( y=kf(a(x+b))+c \), where a, b, c and k are constants, in a variety of contexts, where \( f(x) \) is one of \( \sin x \), \( \cos x \) or \( \tan x \), stating the domain and range when appropriate
  • use technology or otherwise to examine the effect on the graphs of changing the amplitude (where appropriate), \( y=kf(x) \), the period, \( y=f(ax) \), the phase, \( y=f(x+b) \), and the vertical shift, \( y=f(x)+c \)
  • use k, a, b, c to describe transformational shifts and sketch graphs
• Solve trigonometric equations involving functions of the form kf(a(x+b))+c, using technology or otherwise, within a specified domain
• Use trigonometric functions of the form \( kf(a(x+b))+c \) to model and/or solve practical problems involving periodic phenomena