How do I find the phase shift of a sinusoidal graph?

1 Answer
Jun 19, 2015

Answer:

Find the value of #x# at which we find #sin(0)#.

Explanation:

Examples:

#y=3+2sin(3x- pi/4)#

Solve: #3x-pi/4 = 0#

So #x= pi/12# is the shift.

#y=5-sin(4x+ pi/2)#

Solve: #4x + pi/2 = 0#

So #x= -pi/8# is the shift.

#y=-3sin(pix+ (3pi)/4)#

Solve: #pix + (3pi)/4 = 0#

So #x= -3/4# is the shift.

Some textbooks use:
#y = asin(bx+c)# has phase shift #-c/b#

Other textbooks use:
#y = asin(bx-c)# has phase shift #c/b#

For me (having taught out of both kinds of textbook), it's easier just to solve the equation.