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Question

Sketch the following graphs :
(i) y=cos(x+π4)
(ii) y=cos(xπ4)
(iii) y=3cos(2x1)
(iv) y=2cos(xπ2)


Solution

(i) We have,
y=cos(x+pi4)
y0=cos(x+π4)
y0=cos(x+π4) .....(i)
Shifting the origin at (π4,0) we obtain 
x=Xπ4,y=Y+0
Substituting these values in (i), we get Y=cos X.
Thus we draw the graph of Y=cos X and shift it by π4 to left to get the required graph. 


(ii) We have, 
y= cos (xπ4)
y0= cos (xπ4) ....(i)
Shifting the origin at (π4,0), we obtain
x=Xπ4,y=Y+0
Substituting these values in (i), we get 
Y= cos X.
Thus we draw the graph of Y= cos X and shift it by π4 to the right to get the required graph. 


(iii) We have, 
y= 3 cos (2x-1)
(y0)=3 cos 2(x12)
Shifting the origin at (12,0), We have 
x=X=13 and y=Y+0
Substituting these values in (i), we get 
Y=3 cos 2X
Thus we draw the graph of Y= 3 cos 2x and shift it by 12 to the right to get the required graph. 


(iv) We have, 
y=2cos(xπ2)
y0=2cos(xπ2)...(i)
Shifting the origin at (π2,0), we obtain
x=X+π4,y=Y+0
Substituting these values in (i), we get 
Y=2 cos X. 
Thus we draw the graph of Y=2cos X and shift it by π2 to the right to get the required graph.

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