Question

# Sketch the following graphs : (i) y=cos(x+π4) (ii) y=cos(x−π4) (iii) y=3cos(2x−1) (iv) y=2cos(x−π2)

Solution

## (i) We have, y=cos(x+pi4) ⇒y−0=cos(x+π4) ⇒y−0=cos(x+π4) .....(i) Shifting the origin at (−π4,0) we obtain  x=X−π4,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 (x−π4) ⇒y−0= cos (x−π4) ....(i) Shifting the origin at (π4,0), we obtain x=X−π4,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) ⇒(y−0)=3 cos 2(x−12) 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(x−π2) ⇒y−0=2cos(x−π2)...(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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