Transformations+of+Trigonometric+Functions

November 7, 2011 by: Rejy

Transformations on Trigonometric Functions


 * Vertical Stretch / Change in Amplitude**
 * If y=a //sin// then |a|=amplitude
 * If a<0 then the graph is reflected on the x axis
 * eg :


 * Vertical Translation**
 * If y=sinx + c then the graph y=sinx is translated |c| units up if c>0 and |c| units down if c<0
 * eg :




 * Horizontal Translation / Phase shift**
 * If y=sin (x-d) then the graph of y=sinx is translated |d| units to the right if d>0 and d units left if d<0
 * eg :




 * Horizontal Srtetch / Change in Period**
 * If y=sin kx then the period of the function is 2** π/  **** k **
 * eg :




 * Combination of Transformations:**

y=2sin (x/2 + ** π/8) +  ** 3 y=2sin(1/2(x + ** π/4)  ** + 3  amplitude=2  period=4 **  π  ** phase shift= **  π/4  ** left  vertical shift= 3 up  min = 1 max=5