# Exploring Sine Waves

- Author:
- Mary O'Malley

## The formula for sine waves can be modeled by the function f(x) = a * sin(b(x - h)) + k. Use the sliders one at a time to investigate how each letter in the equation affects the graph of f(x).

Investigate the slider with the 'a' value. How does the value of 'a' affect the sine graph? Be sure to comment on both positive and negative values of a.

## Part 2

Investigate the slider with the 'b' value. How does the value of 'b' affect the sine graph?

## Part 3

Investigate the sliders with both the 'h' and the 'k' values. Describe how these values affect the sine graph.

## Part 4

## Challenge

Above you see two sine waves - the purple wave controlled directly to the sliders and the yellow wave which is related to the purple wave. Move the sliders to investigate the relationship between the two functions. How are the two equations related? (Hint: It will greatly help to write down the equations for both the purple and yellow equations for a few examples to study the difference)