Chapter 6: Graphs of Trigonometric Functions – Exercise 6.2

Graphs of Trigonometric Functions – Exercise 6.2 – Q.1

We have,

Substituting these values in (i), we get

Y = cost X.

Thus we draw the graph of Y = cos X and shift it by π/4 to the left to get the required graph.

We have,

Substituting these values in (i), we get

Y = cos X.

Thus we draw the graph of Y = cos X and shift it by π/4 to the left to get the required graph.

We have,

Y = 3 cos 2X.

Thus we draw the graph of Y = 3 cos 2 X and shift it by 1/2 to the left to get the required graph.

We have,

Substituting these values in (i), we get

Y = 2 cos X.

Thus we draw the graph of Y = 2 cos X and shift it by π/2 to the left to get the required graph.

Graphs of Trigonometric Functions – Exercise 6.2 – Q.2

We have,

Substituting these values in (i), we get

Y =  cos 2X.

Thus we draw the graph of Y = 2 cos X and shift it by π/4 to the left to get the required graph.

To obtain the graph of y = cos x/2 we first draw the graph of y = cos x in the interval [0, 2π] and then divide the x-coordinates of the points where it crosses x-axis by 1/2.