![Graphs of sin , cos , tan
also called trig functions
sin( ) sin( ) sin( )
Note: as we change , different values of sin result
Let =x
Resulting values are Dependent variable, ie. y
So we get,
f( ) = sin
Let's graph f( ) = sin over [0, 2 ]](https://image.slidesharecdn.com/newday8examples-130307164813-phpapp02/85/New-day-8-examples-1-320.jpg)
![Definitions
Periodic Function = function whose graph has a pattern
Period = the length of one full pattern.
ex. in sine graph its 2
Amplitude = vertical deviation of graph from middle
(sinusoidal axis).
Sinusoidial Axis = horizontal axis above and below
which the graph fluctuates. It defines the amplitude.
Characteristics of sine function
Domain: In general
Range: In general
Zeroes: In general
Graph f( ) = cos over [0, 2 ]
Domain: In general
Range: In general
Zeroes: In general + k ,k I](https://image.slidesharecdn.com/newday8examples-130307164813-phpapp02/85/New-day-8-examples-3-320.jpg)
![Graph f( ) = tan over [-2 ,2 ]
Locating the zeroes:
f( ) = 0
ie. tan = 0
sin = 0
when sin = 0, occurs when = 0, , 2 , - , -2
What happens when cos = 0
in tan = sin = sin =
- an invisible line where the graph or function is undefined
when cos = 0, occurs when = , 3 , - , -3
Domain: In general
Range: In general
Equations for asymptotes: x =](https://image.slidesharecdn.com/newday8examples-130307164813-phpapp02/85/New-day-8-examples-4-320.jpg)
New day 8 examples
- 1. Graphs of sin , cos , tan also called trig functions sin( ) sin( ) sin( ) Note: as we change , different values of sin result Let =x Resulting values are Dependent variable, ie. y So we get, f( ) = sin Let's graph f( ) = sin over [0, 2 ]
- 3. Definitions Periodic Function = function whose graph has a pattern Period = the length of one full pattern. ex. in sine graph its 2 Amplitude = vertical deviation of graph from middle (sinusoidal axis). Sinusoidial Axis = horizontal axis above and below which the graph fluctuates. It defines the amplitude. Characteristics of sine function Domain: In general Range: In general Zeroes: In general Graph f( ) = cos over [0, 2 ] Domain: In general Range: In general Zeroes: In general + k ,k I
- 4. Graph f( ) = tan over [-2 ,2 ] Locating the zeroes: f( ) = 0 ie. tan = 0 sin = 0 when sin = 0, occurs when = 0, , 2 , - , -2 What happens when cos = 0 in tan = sin = sin = - an invisible line where the graph or function is undefined when cos = 0, occurs when = , 3 , - , -3 Domain: In general Range: In general Equations for asymptotes: x =