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

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 )

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 )

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 )