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10.2.3  Increasing the phase by π/2 in a trigonometric expression

The shift_phase command increases the phase of a trigonometric expression by π/2.

Examples

shift_phase(x+sin(x))
     
xcos


π +2 x
2



          
shift_phase(x+cos(x))
     
x+sin


π +2 x
2



          
shift_phase(x+tan(x))
     
x
1
tan


π +2 x
2



          

Quoting the argument will prevent the automatic simplification.

shift_phase('sin(x+pi/2)')
     
cos


π +2 x+2 
π
2
2



          

With an unquoted sine, you get:

shift_phase(sin(x+pi/2))
     
sin


π +2 x
2



          

since sin(x+pi/2) is evaluated (in this case simplified) before shift_phase is called, and shift_phase(cos(x)) returns sin((pi+2*x)/2).


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