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Graphs Of Trigonometric Functions

Class 11th Mathematics RS Aggarwal Solution
Exercise 19
  1. Sin 3x Draw the graph of each of the following functions:
  2. 3sin x Draw the graph of each of the following functions:
  3. 2sin 3x Draw the graph of each of the following functions:
  4. 2cos 3x Draw the graph of each of the following functions:
  5. sin {x}/{2} Draw the graph of each of the following functions:
  6. Draw the graphs of y = sin x and y = cosξ n[0 , 2 pi ] on the same axes.…
  7. Draw the graphs of y = cos x and y = cos2x[0 , 2 pi ] on the same axes.…
Exercise 19
Question 1.

Draw the graph of each of the following functions:

Sin 3x
Answer:

To draw the graph of the curve sin(3x) assume some standard angle measures which will help in locating the points and drawing the curve.



Therefore, the graph of curve sin(3x) can be drawn as



Here, the frequency of the function sin(x) is increased by 3 times.
Question 2.

Draw the graph of each of the following functions:

3sin x
Answer:

To draw the graph of the curve 3sin(x) assume some standard angle measures which will help in locating the points and drawing the curve.



Therefore, the graph of curve 3sin(x) can be drawn as



Here, the amplitude of the function sin(x) is increased by 3 times.
Question 3.

Draw the graph of each of the following functions:

2sin 3x
Answer:

To draw the graph of the curve 2sin(3x) assume some standard angle measures which will help in locating the points and drawing the curve



The graph looks like:
Question 4.

Draw the graph of each of the following functions:

2cos 3x
Answer:

To draw the graph of the curve 2cos(3x) assume some standard angle measures which will help in locating the points and drawing the curve.



Therefore, the graph of curve 2cos(3x) can be drawn as



Here, the amplitude and frequency of the function cos(x) is increased by 2 and 3 times respectively.
Question 5.

Draw the graph of each of the following functions:
Answer:

To draw the graph of the curve sin(x/2) assume some standard angle measures which will help in locating the points and drawing the curve.



Therefore, the graph of curve 2cos(3x) can be drawn as



Here, the frequency of the function sin(x) is decreased by 0.5 times.
Question 6.

Draw the graphs of y = sin x and on the same axes.
Answer:

For sinx



For cosx




The green line represents curve for sin(x) and blue for cos(x) for [0,2π].
Question 7.

Draw the graphs of y = cos x and on the same axes.
Answer:

For cosx



For cos(2x)



The graph is:-



Blue line depicts curve cos(2x)


Purple lines depict cos(x).