Chapter 6: Graphs of Trigonometric Functions – Exercise 6.1

Graphs of Trigonometric Functions – Exercise 6.1 – Q.1

To obtain the graph of y = 3 sin x we first draw the graph of y = sin x in the interval [0, 2x]. The maximum and minimum values are 3 and - 3 respectively.

We have,

Substituting these values in (i), we get

Y = 2sin x

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

We have,

Substituting these values in (i), we get

Y = 2sin 2X

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

We have,

Substituting these values in (i), we get

Y = 2sin 3X

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

We have,

Substituting these values in (i), we get

Y = 3 sin 2X

Thus we draw the graph of Y = 3 sin 2X and shift it by 1/8 to the right to get the required graph.

 

Graphs of Trigonometric Functions – Exercise 6.1 – Q.2

We have,

Substituting these values in (i), we get

Y = sin X.

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

To obtain the graph of y = sin 3x we first draw the graph of y = sin x in the interval [0, 2π] and then divide the x-coordinates of the points where it crosses x-axis by 3.