Graph of y = 1 - cos ( pi/4 - x )

y = 1 - cos ( pi/4 - x )
= 1 - cos [ - ( x - pi/4 )]
Formula : cos ( - x ) = cos x
so y = 1 - cos ( pi/4 - x )
= 1 - cos [ - ( x - pi/4 )]
= 1 - cos ( x - pi/4 )
Step 1: Draw the graph of y = cos x
Draw the graph of y = cos x
when x = 0, y = cos x = cos 0 = 1, y is maximum
when x = pi/2, y = cos x = cos pi/2 = 0
when x = pi, y = cos x = cos pi = -1, y is minimum
Step 2: Draw the graph of y = cos ( x - pi/4 )
Right shift y = cos x  pi/4 to get the graph of y = cos ( x - pi/4 )
Draw the graph of y = cos(x - pi/4)
when x = pi/4, y = cos ( x - pi/4 ) = cos ( pi/4 - pi/4 ) = cos 0 = 1, y is maximum
when x = 3pi/4, y = cos ( x - pi/4 ) = cos ( 3pi/4 - pi/4 ) = cos 2pi/4 = cos pi/2 = 0
Step 3: Draw the graph of y = - cos ( x - pi/4 )
Refletion the graph of y = cos (x - pi/4) in the x-axis to get the graph of y = - cos ( x - pi/4 )
Draw the graph of y = -cos(x - pi/4)
Step 4: Draw the graph of y = 1 - cos ( x - pi/4 )
Add one to the graph of y = - cos ( x - pi/4 ) to get the graph of y = 1 - cos ( x - pi/4 )
Draw the graph of y = 1 - cos(x - pi/4)