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
Domain: In general
Range: In general
Equations for asymptotes: x =
=
, 3 , - , -3