The Inverse Trigonometric functions are also called as arcus functions, cyclometric functions or anti-trigonometric functions. These functions are used to obtain angle for a given trigonometric value. Inverse trigonometric functions have various application in engineering, geometry, navigation etc.
Representation of functions:
Generally, the inverse trigonometric function are represented by adding arc in prefix for a trigonometric function, or by adding the power of -1, such as:
Inverse of sin x = arcsin(x) or
Let us now find the derivative of Inverse trigonometric function
Example: Find the derivative of a function
Solution:Given
Differentiating the above equation w.r.t. x, we have:
Putting the value of y form (i), we get
From equation (ii), we can see that the value of cos y cannot be equal to 0, as the function would become undefined.
i.e.
From (i) we have
Using property of trigonometric function,
Now putting the value of (iii) in (ii), we have
Therefore, the Derivative of Inverse sine function is
Derivatives of Inverse trigonometric functions
Function | ( |
arcsin x | |
arccos x | |
arctan x | |
arccot x | |
arcsec x | |
arccsc x |
Example:Find the derivative of a function 2 arcsin x – 5 arccsc x.
Solution:Given Further we can factorize the given expression. Example:Find the derivative of a function Solution:Given y = |
Video Lesson on Trigonometry
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