Graphing the Trig function y = sin x
Let us assume the values for x and find the corresponding values for y.
The following table shows the values of y for the corresponding values of y.
x

 2 $\pi$

3 $\frac{\pi}{2}$

 $\pi$

 $\frac{\pi}{2}$ 
0

$\frac{\pi}{2}$ 
$\pi$ 
3 $\frac{\pi}{2}$ 
2 $\pi$ 
y 
0

1

0

1

0

1

0

1

0

Let us plot these points in the graph and join the points.
From the above graph we observe that
1. The curve is continuous from  2 $\pi$ to + 2$\pi$
2. The curve passes through the origin.
3. The domain consists of all real numbers.
In the above graph Domain = {  2 $\pi$, 2 $\pi$}
4. The graph has its maximum value y = 1 and the min value y = 1.
Therefore, the range of the function is { x : x $\epsilon$ [1, 1 ], x is a Real number }
5. The curve reaches maximum at x =  3 $\frac{\pi}{2}$ and $\frac{\pi}{2}$,
therefore the period of the function is = $\frac{\pi}{2}$  ( 3 $\frac{\pi}{2}$)
= $\frac{\pi}{2}$ + 3 $\frac{\pi}{2}$
= 4 $\frac{\pi}{2}$
= 2 $\pi$
6. The curve is symmetric about the xaxis, distance between the axis of symmetry and the maximum point is 1 unit.
Therefore, amplitude = 1 unit.Graphing Trig Function y = Cos x.
Let us assume the values for x and find the corresponding values for y.
The following table shows the values of y for the corresponding values of y.
x
  2 $\pi$
 3 $\frac{\pi}{2}$   $\pi$
  $\frac{\pi}{2}$  0
 $\frac{\pi}{2}$  $\pi$  3 $\frac{\pi}{2}$  2 $\pi$ 
y  1
 0
 1
 0
 1
 0
 1
 0
 1

From the above graph we observe that
1. The curve is continuous from  2 $\pi$ to + 2$\pi$
2. The curve does not pass through the origin.
3. The domain consists of all real numbers.
In the above graph Domain = { x : x $\epsilon$ [  2 $\pi$, 2 $\pi$ ] }
4. The graph has its maximum value y = 1 and the min value y = 1.
Therefore, the range of the function is { x : x $\epsilon$ [1, 1 ], x is a real number }
5. The curve reaches maximum at x =  2 $\frac{\pi}{2}$ and x = 0
therefore the period of the function is = 0  (  2 $\pi$ )
= 2 $\pi$
= 2 $\pi$
6. The curve is symmetric about the xaxis, distance between the axis of symmetry and the maximum point is 1 unit.
Therefore, amplitude = 1 unit.Graphing Trig function y = Tan x.
Let us assume the values for x and find the corresponding values for y.
The following table shows the values of y for the corresponding values of y.
From the above graph we observe that
1. The curve is continuous from  $\frac{\pi}{2}$ to + $\frac{\pi}{2}$ and is not continuous at all real numbers.
2. The graph does not touch the line x = n $\frac{\pi}{2}$ where n is an integer. Hence the function is not defined when x = n $\frac{\pi}{2}$.
2. The curve passes through the origin.
3. The domain consists of real numbers between $\frac{\pi}{2}$ and $\frac{\pi}{2}$..
In the above graph Domain = ( 3$\frac{\pi}{2}$,  $\frac{\pi}{2}$) , ($\frac{\pi}{2}$, $\frac{\pi}{2}$) , ($\frac{\pi}{2}$, 3$\frac{\pi}{2}$),
4. The graph has its maximum value which is + $\infty$ and the minimum value which is  $\infty$.
Therefore, the range of the function is { x : x $\epsilon$ ( $\infty$, $\infty$ ) }
5. The curve reaches infinity at x = $\frac{\pi}{2}$ and $\frac{\pi}{2}$,
therefore the period of the function is = $\frac{\pi}{2}$  ( $\frac{\pi}{2}$)
= $\frac{\pi}{2}$ + $\frac{\pi}{2}$
= $\pi$
6. The curve is symmetric about the yaxis.