What are the derivatives of the 6 trig functions?

What are the Derivatives of the 6 Trig Functions?

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

What is the integral of cosine?

By the fundamental theorem of calculus and the fact that the derivative of sin(x) is cos(x), we have that the integral of cos(x) is sin(x) + C, where C is a constant.

What are the 3 trigonometric identities?

Sine, cosine and tangent are the primary trigonometry functions whereas cotangent, secant and cosecant are the other three functions….The reciprocal trigonometric identities are:

  • Sin θ = 1/Csc θ or Csc θ = 1/Sin θ
  • Cos θ = 1/Sec θ or Sec θ = 1/Cos θ
  • Tan θ = 1/Cot θ or Cot θ = 1/Tan θ

How do you differentiate trigonometric functions?

Trigonometric Function Differentiation

  1. If f( x) = sin x, then f′( x) = cos x.
  2. If f( x) = cos x, then f′( x) = −sin x.
  3. If f( x) = tan x, then f′( x) = sec 2 x.
  4. If f( x) = cot x, then f′( x) = −csc 2 x.
  5. If f( x) = sec x, then f′( x) = sec x tan x.
  6. If f( x) = csc x, then f′( x) = −csc x cot x.

Are basic trigonometry functions?

The basics of trigonometry define three primary functions which are sine, cosine and tangent . Trigonometry is one of those divisions in mathematics that helps in finding the angles and missing sides of a triangle with the help of trigonometric ratios. The angles are either measured in radians or degrees.

What are the trigonometric functions?

Trigonometric functions: Sine, Cosine, Tangent, Cosecant, Secant, Cotangent. In mathematics, the trigonometric functions are a set of functions which relate angles to the sides of a right triangle.

How do I simplify the trigonometric function?

To simplify a trigonometric expression, enter the expression to simplify and apply the trig_calculator function . Thus, for the simplification of the following expression cos ( x + π) + 2 ⋅ sin ( x), enter trig_calculator ( cos ( x + π) + 2 ⋅ sin ( x)) , after calculation the simplified form of the trigonometric expression is returned.

Can I Divide by cosine in a trig function?

In summary, unless you get a tangent (or in some cases, a cotangent) when you divide by a cosine (or in some cases, sine), DO NOT EVER DIVIDE BY A TRIGO FUNCTION!