Class 11 Maths Chapter 13 Notes
Important Complete Class 11 Maths Chapter 13 Notes written by Professor Asad Khalid Suib. These notes are very helpful in the preparation of Mathematics for first-year students and these are according to the paper patterns of all Colleges in the World.
Summary and Contents:
Topics which are discussed in the notes are given below:
- Our comprehensive Class 11 Maths Chapter 13 Notes will ensure you're fully prepared for your exams.
- All solved exercises of chapter Number. 13: Inverse Trigonometric Functions in the 1st year of the Punjab Textbook Boards.
- The inverse sine function
- Principle Sine 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
- Domains and range of trigonometric functions
- Solution of each question in Exercise 13.1 in the 1st year of the Punjab Textbook Boards.
- Solution of each question in Exercise 13.2 in the 1st year of the Punjab Textbook Boards.
- Note. While discusspjpihe Inverse Trigonometric Functions, we have seen that there are in general, no inverses of Trigonometric Functions, but restricting their domain to principal Functions, we have made them as functions.
- Domains and Ranges of Principal Trigonometric Function: and Inverse Trigonometric Functions. From the discussion on the previous pages we get the following table showing domains and ranges of the Principal Trigonometric and Inverse Trigonometric Functions.
- The graph of y = tanx, -T< x < +T, is shown in the igure 7. We observe that every horizontal line between the lines y = 1 and y = -1 intersect the graph ininitly many times. It follows that the tangent function is not one-to-one. However, if we restrict the domain of y = Tanx to the interval , then the restricted function y = tanx , is called the Principal tangent function; which is now one-to-one and hence will have an inverse as shown in igure 8. This inverse function is called the inverse tangent function and is written as tan-1x or arc tanx. The Inverse Tangent Function is deined by: y = tan-1x , if and only if x = tan y. where and - < < - ∞ < < +∞ . Here y is the angle whose tangent is x. The domain of the function y = tan-1x is -T< x <+T and its range is The graph of y = tan-1x is obtained by relecting the restricted portion of the graph of y = tanx about the line y = x as shown in igure 9. We notice that the graph of y = tanx is along the x - axis whereas the graph of y = tanx is along the y- axis.
- We observe that every horizontal line between the lines y = 1 and y= -1 intersects the graph ininitly many times. It follows that the sine function is not one-to-one.However, if we restrict the domain of y = sinx to the interval , then the restricted function y = sinx, is called the principal sine function; which is now one-to-one and hence will have an inverse as shown in igure 2. This inverse function is called the inverse sin function and is written as sin-1x or arcsinx. The Inverse sine Function is deined by: y = sin-1x , if and only if x = sin y. where and Here y is the angle whose sine is x. The domain of the function y = sin-1x is - 17 x 7 1, its range is The graph of y = sin-1x is obtained by relecting the restricted portion of the graph of y = sinx about the line y = x as shown in igure 3. We notice that the graph of y = sinx is along the x - axis whereas the graph of y = sin-1x is along the y - axis.