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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.

Graph of y = 3 sin

We have,

Graphs of Trigonometric Functions – Exercise 6.1 – Q.1

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.

Graph of Y = 2

We have,

graphs-of-trigonometric-functions–exercise-6.1–q.1(i)

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.

The graph of Y = 2

We have,

graphs-of-trigonometric-functions–exercise-6.1–q.1(ii)

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.

The graph of Y = 3

We have,

graphs-of-trigonometric-functions–exercise-6.1–q.1(iii)

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.

The graph of Y = 3 sin

 

Graphs of Trigonometric Functions – Exercise 6.1 – Q.2

Graphs of Trigonometric Functions – Exercise 6.1 – Q.2

We have,

graphs-of-trigonometric-functions–exercise-6.1–q.2(i)

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.

obtain the graph of y = sin 3x


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