4.5 Graphs Of Sine And Cosine Functions
When using a calculator,make sure that you are in radians when graphing!!!!
Sine
When y=sin x
- The range of the function is [-1,1]
- The domain of the function is negative infinity to infinity.
- the period is 2╥
Cosine
When y=cos x- The range of the function is [-1,1]
- The domain of the function is negative infinity to infinity.
- the period is 2╥
Changes To The Graphs
y=a sin(bx-c) +dy=a cos(bx-c) +d
Changes In A
Changes in a affect the amplitude
The amplitude is half the distance between the maximum and minimum values of the functionThe larger a is, the larger the amplitude will be.
When a is negative the graph is reflected about the x-axis
This is the graph of y=2 sin x
Changes In B
Changes in b affect the period
If b is between 0 and 1 the period will be greater than 2╥
The graph is horizontally stretched.
If b is greater than one the period is less than 2╥
The graph is horizontally compressed.
If b is negative than we can use sin(-x)=-sin x and cos(-x)=cos x to figure out what the new equation and graph look like.
This is the graph of y=(-4x) compared to the graph of y=sin x
Changes In C And D
Changes in c and d have to do with horizontally and vertically translating the graphs.
When c is positive the graph is horizontally translated to the left
When c is negative the graph is horizontally translated to the right
When d is positive the graph is vertically translated to the right
When d is negative the graph is vertically translated to the left
This graph shows how each variable changes the graph.