What can we tell about the graph of inverse Trigonometric function which r even & which one r odd

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Solution

Dear Student

To see which functions are odd and which are even from graph there is same method for all whether they are rational functions or inverse trigonometrical functions. Graphs which are symmetric about the origin and the value of function remains unchanged when graph is rotated by 180 degree about origin are called odd functions whereas graphs which are symmetrical about y-axis are called even function. The graphs which are not satisfying any of the above conditions are neither even nor odd.
Among inverse trigonometric functions arcsin, arctan, arccosecant are odd functions while arccos, arccot, arcsecant are neither odd nor even functions. There is no even inverse trigonometric function.

Regards

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corresponding graph of original function as a mirror image (i.e., reflection) along which line ?

Q. Inverse trigonometric functions have restricted domain and range, [.] and |.| denotes greatest integer function and modulus function respectively, then

\begin{matrix} I n v e r s e T r i g o n o m e t r i c & D o m a i n & R a n g e F u n c t i o n y = s i n^{- 1} x & x ϵ [- 1, 1] & y ϵ [\frac{- π}{2}, \frac{π}{2}] y = c o s^{- 1} x & x ϵ [- 1, 1] & y ϵ [0, π] y = t a n^{- 1} x & x ϵ R & y ϵ (\frac{- π}{2}, \frac{π}{2}) y = c o t^{- 1} x & x ϵ R & y ϵ (0, π) y = s e c^{- 1} x & x ϵ R - (- 1, 1) & y ϵ [0, π] - {\frac{π}{2}} y = c o s e c^{- 1} x & x ϵ R - (- 1, 1) & y ϵ [\frac{- π}{2}, \frac{π}{2}] \end{matrix}

The equation

s i n^{- 1} x = | x - a |

will have at least one solution, if

If we consider only the principle values of the inverse trigonometric functions, then the value of $t a n (c o s^{- 1} \frac{1}{5 \sqrt{2}} - s i n^{- 1} \frac{4}{\sqrt{17}})$

Which of the following is/are incorrect?
a) Graph tells the linear variation between two quantities.
b) In Histogram , we can have different width of the bar.
c) Pie chart , tells the comparison within one unit.
d)Linear graph can be discontinuous.

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