Class 11 Maths Chapter 11 Notes
Handwritten notes of Class 11 Maths Chapter 11 Notes written by Professor M. Sulman Sherazi Suib. These notes are very helpful in the preparation of Trigonometric Functions and Their Graph for the students of Mathematics of the Intermediate and these are according to the paper patterns of all Punjab boards.
Summary and Contents:
Topics which are discussed in the notes are given below:
- Our comprehensive Class 11 Maths Chapter 11 Notes will ensure you're fully prepared for your exams.
- Definition of a domain of a function
- Definition range of function
- Graph of a sine function
- Graph of a cosine function
- Graph of the tangent function
- Graph of the cotangent function
- Graph of the cosecant function
- Graph of the secant function
- Definition of function with examples
- Definition of into function with examples
- Definition of objective function with examples
- Definition of injective function with examples
- Definition of bijective function with examples
- Inverse trigonometric functions
- The inverse sine function
- Principle and function
- inverse principle Sine function
- Properties of inverse principle sine function
- The inverse Cosine function
- The inverse Tangent function
- The inverse Cotangent function
- The inverse Cosecant function
- The inverse Secant function
- For this purpose,
- i) table of ordered pairs (x, y) is constructed, when x is the measure of the angle and
- y is the value of the trigonometric ratio for the angle of measure x;
- ii) The measures of the angles are taken along the X- axis;
- iii) The values of the trigonometric functions are taken along the Y-axis;
- iv) The points corresponding to the ordered pairs are plotted on the graph paper,
- v) These points are joined with the help of smooth ciurves.
- Note: As we shall see that the graphs of trigonometric functions will be smooth curves and none of them will be line segments or will have sharp corners or breaks within their domains. This behaviour of the curve is called continuity. It means that the trigonometric functions are continuous, wherever they are deined. Moreover, as the trigonometric functions are periodic so their curves repeat after a ixed interval.
- We know that the period of the tangent function is p . The graph is extended on both sides of x-axis through an interval of p in the same pattern and so we obtain the graph of y = tan x from -360° to 360° as shown below:
- Note 1: From the graphs of trigonometric functions we can check their domains and ranges.
- Note 2: By making use of the periodic property, each one of these graphs can be extended on the left as well as on the right side of x-axis depending upon the period of the functions.
- Note 3: The dashes lines are vertical asymptotes in the graphs of tan x, cot x, sec x and csc x.
- On the same axes and to the same scale, draw the graphs of the following function for their complete period: i) y = sinx and y = sin2x ii) y = cosx and y = cos2x
- Graph of y = csc x from -2pi to 2pi: We know that: csc ( -x) = - csc x and csc (p - x) = csc x So the values of csc x for x = 0°, 30°, 45°, 60°, can help us in making the following table of the ordered pairs for drawing the graph of y = csc x for the interval 0° to 360°:
- Graph of y = sec x from -2pi to 2pi: We know that sec (-x) sec x and sec (pi -x ) = sec x ,So the values of sec x for x = 0°, 30°, 45°, 60°, can help us in making the following table of the ordered pairs for drawing the graph of y = sec x for the interval 0° to 360°: