# Graphing Trig Functions

- Author:
- Marc Azara

- Topic:
- Trigonometric Functions

## Use the sliders to investigate the graph y=asin(bx)

## Use the sliders for a and b, discuss the following:

- what happens to the amplitude as you change the value of a?
- what happens to the period as you change the value of b?
- Summarise your findings
EXTENSION: Graph y = asin(bx+c) and discuss the effect of changing the value of c.

## Use the sliders to investigate the graph of y=acos(bx)

## Use the sliders for a and b, discuss the following:

- what happens to the amplitude as you change the value of a?
- what happens to the period as you change the value of b?
- Summarise your findings
EXTENSION: Graph y = acos(bx+c) and discuss the effect of changing the value of c.

## Use the sliders to investigate the graph of y=atan(bx)

## Use the sliders for a and b, discuss the following:

- what happens to the amplitude as you change the value of a?
- what happens to the period as you change the value of b?
- Summarise your findings
EXTENSION: Graph y = atan(bx+c) and discuss the effect of changing the value of c.

## EXTENSION: Use the input bar to compare the graphs of y=sin(x) and y=cos(x + c) (and likewise for cosx against sin(x+c)

## What did you discover?

- what value of c will make y=cos(x+c) the same as y = sinx?
- what value of c will make y=sin(x+c) the same as y = cosx?
- How does this relate to the right-triangle definitions of sine and cosine?
- Summarise your findings