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May 27, 2024

Learn in Detail About Derivatives of Trigonometric Function and Its Applications

Trigonometric Function

In mathematics, finding the trigonometric functions’ derivatives is a challenging task but it is important for students to find the same. But this process is called the differentiation of trigonometric functions. Calculating the Derivatives of Trigonometric Function means you are measuring the rate of change of that trigonometric function with respect to their variable. Currently, in mathematics we have six different functions that can be used in different derivative problems. Also, they have different differentiation formulas that can be used in different applications of the derivatives. 

We are talking about different trigonometric functions like: sin x, cos x, tan x, cot x, sec x and cosec x. In this post, we will be discussing more about trigonometric functions, Applications of Derivatives in different sectors. They have relevant applications in different sectors because of which we have curated this post. Keep reading to know what derivatives of trig functions are there.

In a Nutshell: Trigonometric Functions’ Differentiation 

In mathematical trigonometry, there is a certain process to calculate the rate of change of trigonometric functions. In functions, the variable part changes accordingly. It means the ‘x’ and ‘y’ part of the function will be changing. However, you don’t need to do rocket science to calculate the derivatives of trigonometric functions. Below we have curated certain derivation of those crucial six trigonometric functions. You can use them while solving different derivative questions.  

  • Derivation of sin x = cos x
  • Derivative of cos x = -sin x
  • Derivative of tan x = sec2 x
  • Derivative of cot x = -cosec2 x
  • Derivative of sec x = sec x. tan x
  • Derivative of cosec x = -cosec x. cot x

So, have you understood about derivatives? To know who they are derived from and what basic fundamentals are involved in it, refer to your textbooks and different study materials.

Differentiation of Trigonometric Functions: Know about applications

In the field of mathematics, every concept has its own application. Likewise, differentiation of trigonometric functions also carries value in the real world, and below we have curated some of the mathematical applications of the same. 

  • It helps in calculating the tangent line slope of the to a trigonometric curve y = f(x).
  • It helps in calculating the normal line’s slope to a trigonometric curve y = f(x).
  • It helps in calculating the tangent line’s equation of the or normal line of a curve.
  • Besides, scientific fields like electronics, programming, modelling of different cyclic functions and many more are based on differentiation of trigonometric functions. 
  • To determine the maximum and minimum values of particular functions, we use the derivatives of trigonometric functions.

How to study trigonometric functions and their derivatives?

Having the basic fundamental knowledge is the key to your success. You cannot ignore the important fundamentals, rules, and important trigonometric identities. Make a list of all identities and revise them regularly. You have to clear all your concepts before solving questions. 

Moreover, sine and cosine rules are something on which most of the trigonometric concepts are based. Therefore, learn them thoroughly. And only learning is not very sufficient. You have to practice relevant questions daily so that you can boost your knowledge retention power. 

Many of you might be having the basic trigonometric table that contains all values and figures. Do not ignore them and practice it regularly.

Supurna Sinha has been working with writing challenged clients for over three years. She writes SEO articles for businesses that want to see their Google search rankings surge. Her educational background in science has given her a broad base from which to approach many topics.