#1**+10 **

y=-1/2sin[4(x+pi/4)]+1

You can build these up bit by bit. You DO need to know what y=sinx looks like

y=sinx has a frequency of 2pi

y=sin4x Will have a frequency of 2pi/4

The point (0,0) on the curve sin4x will be moved to (-pi/4,0) on sin(4(x+pi/4)

That is, the phase shift will be pi/4 to the left.

y=sinx has an amplidude of 1. It oscilates between y=-1 and y=1

y=1/2 sinx has an amplitude of 1/2

and y=-1/2sin x will reflect it across the x axis (turn it upside down)

The plus one ar the end will lift the whole curve up by one.

So instead of it oscillating between y=-0.5 and 0.5 it will oscillate between y=0.5 and 1.5

I can show you these steps on a Desmos graph

I will only show the sine graph at the beginning then I will step through the building of the final graph one step at the time.

Each graph can be displayed (or made invisable again) by clicking the circle in front of its formula

Melody
Jul 2, 2015

#1**+10 **

Best Answer

y=-1/2sin[4(x+pi/4)]+1

You can build these up bit by bit. You DO need to know what y=sinx looks like

y=sinx has a frequency of 2pi

y=sin4x Will have a frequency of 2pi/4

The point (0,0) on the curve sin4x will be moved to (-pi/4,0) on sin(4(x+pi/4)

That is, the phase shift will be pi/4 to the left.

y=sinx has an amplidude of 1. It oscilates between y=-1 and y=1

y=1/2 sinx has an amplitude of 1/2

and y=-1/2sin x will reflect it across the x axis (turn it upside down)

The plus one ar the end will lift the whole curve up by one.

So instead of it oscillating between y=-0.5 and 0.5 it will oscillate between y=0.5 and 1.5

I can show you these steps on a Desmos graph

I will only show the sine graph at the beginning then I will step through the building of the final graph one step at the time.

Each graph can be displayed (or made invisable again) by clicking the circle in front of its formula

Melody
Jul 2, 2015

#2**+5 **

I like that presentation, Melody......it really shows how each component of the function changes the shape/orientation of the curve.....!!!!

CPhill
Jul 2, 2015

#3**+5 **

Thanks Chris,

I had very good maths teachers when I was at school (most of the time). I am very grateful to them because these formative years are very important to learn the concepts and also for teaching the concepts at a later time.

This building up of graphs was not taught to me at school, perhaps the rudiments of it were but I mostly worked it out for myself. It is an incredibly useful concept to understand. And it is fun seeing the graphs 'grow' from the germ of a beginning.

Desmos graphing calculator is a fantastic tool to show how the procedure works :)

Melody
Jul 2, 2015