Transformation Of Trigonometric Graphs

1. If $a>0$ : Scaling of graph with a factor of $a$ parallel to the $y$ -axis
2. If $a<0$ : Scaling of graph with a factor of $a$ parallel to the $y$ -axis, then reflecting of graph in $x$ -axis
For sin & cos: amplitude becomes $|a|$
For tan: there is no amplitude
$\text{amplitude}=\dfrac{\text{maximum} -\text{minimum}}{2}$

Scaling of graph with a factor of $\dfrac{1}{b}$ parallel to the $x$ -axis
For sin & cos: period becomes $\dfrac{2\pi}{b}$
For tan: period becomes $\dfrac{\pi}{b}$

Translating of graph by $c$ units parallel to the $y$ -axis
$c=\dfrac{\text{maximum}+\text{minimum}}{2}$

1. $y=sin bx$ : Scaling of graph with a factor of $\dfrac{1}{b}$ parallel to the $x$ -axis
2. $y=a sin bx$ : Scaling of graph with a factor of $a$ parallel to the $y$ -axis (reflecting of graph in $x$ -axis if $a<0$ )
3. $y=a sin bx+c$ : Translating of graph by $c$ units parallel to the $y$ -axis