Question 1154768
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            In the most important and critical part, the answer by the tutor @MathLover1 is  TOTALLY  and  ABSOLUTELY   W R O N G.


            I came to bring the correct answer.



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Obviously, the first question is how to obtain the plot of the function f(x) = sin(x + pi/2) 

                                          from the plot of the parent function y(x) = sin(x).


    The plots of the two function are shown in the Figure below.


The <U>ANSWER</U> is: to get the plot of the function y(x) = sin(x + pi/2), 

               shift the plot of the parent function  by  {{{pi/2}}}  units to the <U>LEFT</U>.


    {{{graph( 360, 360, -7, 7, -2, 2,
          sin(x), sin(x+pi/2)
)}}}


    Plot y(x) = sin(x) (red) and f(x) = sin(x+pi/2) (green)


. . . . . . . . . . . . 


The second question is how to obtain the plot of the function f(x) = sin(x + pi/3) 

                                from the plot of the parent function y(x) = sin(x).


    The plots of the two function are shown in the Figure below.


The <U>ANSWER</U> is: to get the plot of the function y(x) = sin(x + pi/3), 

               shift the plot of the parent function  by  {{{pi/3}}}  units to the <U>LEFT</U>.


    {{{graph( 360, 360, -7, 7, -2, 2,
          sin(x), sin(x+pi/3)
)}}}


    Plot y(x) = sin(x) (red) and f(x) = sin(x+pi/3) (green)



This knowledge is the cornerstone in the subject, therefore, MEMORIZE this rule:


    if the argument in the formula is shifted to the RIGH, then the plot is shifted to the LEFT.

    and vice versa, if the argument in the formula is shifted to the LEFT, then the plot is shifted to the RIGHT.



If at the exam you will answer as @MathLover1  {{{highlight(_M_I_S_T_A_K_E_N_L_Y)}}}  teaches you, then an UNSATISFACTORY score is GUARANTEED to you. 



The sign  {{{highlight(_M_I_S_T_A_K_E_N_L_Y)}}}  means the same as  {{{highlight(_W_R_O_N_G___W_A_Y_)}}}.
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