Transformations of Trigonometric Functions

The video tutorial explains how to graph the function F(x) = sin(x + π/6) + 1 by understanding and applying transformations. It covers calculating the amplitude, period, phase shift, and vertical transformations. The instructor demonstrates graphing each transformation step by step, starting from the phase shift and adjusting the x-axis accordingly. The tutorial concludes with a complete graph of the function, showing two periods and highlighting the importance of understanding each transformation's effect on the graph.

What is the function we are graphing in this tutorial?

• F(x) = sin(x + π/6) + 1

• F(x) = tan(x + π/6) + 1

• F(x) = cos(x + π/6) + 1

• F(x) = sin(x - π/6) + 1

Which parameters are identified in the transformation function?

• a and b

• b and c

• c and d

• a and d

What is the amplitude of the function F(x) = sin(x + π/6) + 1?

• 0

• 1

• 2

• π

How is the period of the function calculated?

• π/a

• 2π/b

• 2π/a

• π/b

What is the phase shift of the function F(x) = sin(x + π/6) + 1?

• -π/6

• π/6

• 0

• 1

What is the vertical translation of the function?

• 1

• -1

• π

• 0

What is the first step in graphing the transformations?

• Calculate the amplitude

• Start at the phase shift

• Determine the period

• Graph the parent function

How many X scales are there in one period?

• 2

• 3

• 4

• 5

What is the distance between each X scale?

• π/2

• π/4

• 2π

• π

What is the reduced form of 8π/6?

• π/3

• 2π/3

• 5π/3

• 4π/3