SOLUTION: Describe the transformation required to obtain the graph of the function f(x)=sin(x+pi/2); g(x)=sin(x+pi/3)

Algebra ->  Trigonometry-basics -> SOLUTION: Describe the transformation required to obtain the graph of the function f(x)=sin(x+pi/2); g(x)=sin(x+pi/3)      Log On


   

Question 1154768: Describe the transformation required to obtain the graph of the function f(x)=sin(x+pi/2); g(x)=sin(x+pi/3)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Describe the transformation required to obtain the graph of the function
f%28x%29=sin%28x%2Bpi%2F2%29
g%28x%29=sin%28x%2Bpi%2F3%29
y+=+A%2Asin%28Bx+-+C%29+%2B+D+ where
Amplitude: A
Period: 2pi+%2F+B
Phase Shift: C+%2F+B+
Vertical Shift (up or down):+D

f%28x%29=sin%28x%2Bpi%2F2%29
g%28x%29=sin%28x%2Bpi%2F3%29
compare and you see that functions have same value of A=1, same value of B=1,same value of +D=0, and different value of C
so,
for f%28x%29 horizontal shift is: C+%2F+B=%28pi%2F2%29%2F1=pi%2F2
for g%28x%29+ horizontal shift is: C+%2F+B=%28pi%2F3%29%2F1=pi%2F3

since C is positive, the graph will appear to shift to the right




Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.

            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. 


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

               shift the plot of the parent function  by  pi%2F2  units to the LEFT.


    


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

               shift the plot of the parent function  by  pi%2F3  units to the LEFT.


    


    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%28_M_I_S_T_A_K_E_N_L_Y%29  teaches you, then an UNSATISFACTORY score is GUARANTEED to you. 



The sign  highlight%28_M_I_S_T_A_K_E_N_L_Y%29  means the same as  highlight%28_W_R_O_N_G___W_A_Y_%29.