What are Inverse Trigonometric Functions?
The inverse trigonometric functions are the inverse functions of the trigonometric functions. There are six inverse trigonometric functions: sin-1, cos-1, tan-1, cosec-1, sec-1, cot-1. The inverse trigonometric functions are also called as arc functions.
Differentiation of Inverse Trigonometric Functions
The derivatives of six inverse trigonometric functions are as follows:
|
Function |
Derivative of Function |
|---|---|
|
sin-1 x |
1/√(1 – x2) |
|
cos-1 x |
-1/√(1 – x2) |
|
tan-1 x |
1/(1 + x2) |
|
cosec-1 x |
1/[|x|√(x2 – 1)] |
|
sec-1 x |
-1/[|x|√(x2 – 1)] |
|
cot-1 x |
-1/(1 + x2) |
Example: Find the derivative of f(x) = 3sin-1x + 4cos-1x
Solution:
f'(x) = (d/dx) [3sin-1x + 4cos-1x]
⇒ f'(x) = (d/dx) [3sin-1x ]+ (d/dx) [4cos-1x]
⇒ f'(x) = 3(d/dx) [sin-1x ]+ 4(d/dx) [cos-1x]
⇒ f'(x) = 3[1 / √(1 – x2)] + 4[-1 / √(1 – x2)]
⇒ f'(x) = 3[1 / √(1 – x2)] – 4[1 / √(1 – x2)]
⇒ f'(x) = [1 / √(1 – x2)] (3- 4)
⇒ f'(x) = -[1 / √(1 – x2)]
Differentiation of Trigonometric Functions
Differentiation of Trigonometric Functions is the derivative of Trigonometric Functions such as sin, cos, tan, cot, sec, and cosec. Differentiation is an important part of the calculus. It is defined as the rate of change of one quantity with respect to some other quantity. The differentiation of the trigonometric functions is used in real life in various fields like computers, electronics, and mathematics.
In this article, we will learn about the differentiation of trigonometric functions along with the formulas, their related proofs, and their applications. Also, we will solve some examples and get answers to some FAQs on the differentiation of trigonometric functions. Let’s start our learning on the topic of Differentiation of Trigonometric functions.
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