Trigonometric Integrals and Derivatives

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Questions and Answers

What is the integral of sin x dx?

-cos x + c

What is the integral of cos x dx?

sin x + c

What is the integral of sec^2 x dx?

tan x + c

What is the integral of csc^2 x dx?

<p>-cot x + c</p> Signup and view all the answers

What is the integral of sec x tan x dx?

<p>sec x + c</p> Signup and view all the answers

What is the integral of csc x cot x dx?

<p>-csc x + c</p> Signup and view all the answers

What is the derivative of sin x?

<p>cos x</p> Signup and view all the answers

What is the derivative of cos x?

<p>-sin x</p> Signup and view all the answers

What is the derivative of tan x?

<p>sec^2 x</p> Signup and view all the answers

What is the derivative of cot x?

<p>-csc^2 x</p> Signup and view all the answers

What is the derivative of sec x?

<p>sec x tan x</p> Signup and view all the answers

What is the derivative of csc x?

<p>-csc x cot x</p> Signup and view all the answers

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Study Notes

Trigonometric Integrals

  • Integral of sin x dx equals -cos x + c, where c is the constant of integration.
  • Integral of cos x dx results in sin x + c.
  • Integral of sec² x dx produces tan x + c.
  • Integral of csc² x dx yields -cot x + c.
  • Integral of sec x tan x dx is sec x + c.
  • Integral of csc x cot x dx results in -csc x + c.

Trigonometric Derivatives

  • The derivative of sin x is cos x.
  • The derivative of cos x is -sin x.
  • The derivative of tan x is sec² x.
  • The derivative of cot x is -csc² x.
  • The derivative of sec x is sec x tan x.
  • The derivative of csc x is -csc x cot x.

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