Yacoubb's 1+2 Methods Thread

[Yacoubb]

Can someone please explain to me everything about sin and cos graphs. I've been away due to being sick and I have no idea how to do any of them. Could someone explain to me what amplitude is (what it means) and what period means and what it is. Also, when doing translations in the x-axis, could someone explain to me what this is? What is a full cycle defined as?


Thanks a lot!

[Tasmania Jones]

Sin and Cos graphs are the graphs of y=sin(x) and y=cos(x)
Graph of y=sin(x)

Graph of y=cos(x)

Amplitude is the furthest distance (maximum height) of the graph from the mid-line (the y-axis is graphs of y=sin(x)). For example, the graph of y=sin(x) has an amplitude of 1.
The period is the length of the 'wave' that repeats itself over and over again. The graph of y=sin(x) has a period of 2 π (radians)

Translations :
For example: y=asin(bx)
a= the amplitude of the graph
b periods will fit into the graph in a distance of 2π; therefore the the period of this function is 2π/b

A full cycle is also known as a period or wavelength and is the section of a graph which repeats itself over and over again.

I hope my explanation is simple yet detailed enough. If I have missed anything others may be able to fill you in.

EDIT: Added diagrams as I felt it would explain it better.