# 08 Transformations Investigation Activity 2

Author:
Jason Lee

## Instructions

Follow the instructions in the questions and move the sliders for n, k and r in the applet accordingly. Answer the questions based on your observations.

## Question 8.1

Shift the slider value for n from n = 1 to n = 4. Describe the resultant transformation of y = cos(x) to y = cos(x - ¼π).

## Question 8.2

With the slider value of n kept at n = 4, shift the slider value for k from k = 1 to k = 2. Describe the resultant transformation of y = cos(x - ¼π) to y = cos(2x - ¼π).

## Question 8.3

With the slider values of n and k kept at n = 4 and k = 2 respectively, shift the slider value for r from r = 1 to r = 3. Describe the resultant transformation of y = cos(2x - ¼π) to y = 3cos(2x - ¼π).

## Question 8.4

What is the amplitude of y = r cos(kx - π/n), if r > 0?

## Question 8.5

What is the period of y = r cos(kx - π/n), if k > 0?

## Question 8.6

Describe a three-step transformation from y = cos(x) to y = cos(2x) - √3sin(2x).

## Question 8.7

What technique did you use in Question 8.6 to work out the three-step transformation?

## Question 8.8

Describe the replacement of variable in each step of your three-step transformation in Question 8.6.