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# Chapter 6: Graphs ofTrigonometric Functions – Exercise 6.3

## Graphs of Trigonometric Functions – Exercise 6.3 – Q.1

We know that

We have,

Substituting these values in (i), we get

Thus we draw the graph of Y = cos 2X, adjust the maximum and minimum values to 1/2 and -1/2 and shift it by 1/2 up to get the required graph.

## Graphs of Trigonometric Functions – Exercise 6.3 – Q.2

We know that

We have,

Substituting these values in (i), we get

Thus we draw the graph of Y = cos 2X, adjust the maximum and minimum values to 1/2 and -1/2 and shift it by 1/2 up to get the required graph.

## Graphs of Trigonometric Functions – Exercise 6.3 – Q.3

We have,

Substituting these values in (i), we get

Y = sin2X.

Thus we draw the graph of Y = sin2 X, and shift it by π/4  to the rught to get the required graph.

## Graphs of Trigonometric Functions – Exercise 6.3 – Q.4

To obtain the graph of y = tan 2x we first draw the graph of y = tan x in the interval and then divide the x-coordinates of the points where it crosses x-axis by 2.

## Graphs of Trigonometric Functions – Exercise 6.3 – Q.5

To obtain the graph of y = tan 3x we first draw the graph of y = tan x in the intervaland then divide the x-coordinates of the points where it crosses x-axis by 3. We then stretch the graph vertically by a factor of 2.

## Graphs of Trigonometric Functions – Exercise 6.3 – Q.6

To obtain the graph of y = 2 cot 2x we first draw the graph of y = cot x in the interval (0, π) and then divide the x-coordinates of the points where it crosses x-axis by 2. We then stretch the graph vertically by a factor of 2.

## Graphs of Trigonometric Functions – Exercise 6.3 – Q.7

We have,

Substituting these values in (i), we get

Y = cos 2X.

Thus we draw the graph of Y = cos 2X, and shift it by π/6 to the  rught to get the required graph.

## Graphs of Trigonometric Functions – Exercise 6.3 – Q.8

We know that

We have,

Thus we draw the graph of Y = cos 2X, adjust the maximum and minimum values to 1/2 and -1/2 and shift it by 1/2 up to get the required graph.