Learning Outcomes

  1. Find the derivatives of sine and cosine functions .
  2. Find the derivatives of the standard trigonometric functions.
  3. Calculate the higher-order derivatives of the sine and cosine functions.

Textbook

  • Chapter 3.5   Derivatives of Trigonometric Functions  

Textbook Assignment

  • p. 285:    177, 179, 185, 187, 191-195 odd

WeBWork Assignment

  • Derivatives-Trigonometric

Exit problems of the session 

  1. Find the derivative of the following functions:

    (a).  f(x)=3\tan x+\dfrac{5}{x}    (b).   g(x)=2\sin x\cos x   (c).  h(x)=\dfrac{\sin x}{1-\cos x}
  2. Find the second order derivative y'' for the given function y=\csc x.

 

Key Concepts

  • Derivative of sine function:    \dfrac{d}{dx}(\sin x)=\cos x
  • Derivative of cosine function:   \dfrac{d}{dx}(\cos x)=-\sin x
  • Derivative of tangent function:   \dfrac{d}{dx}(\tan x)=\sec^2 x
  • Derivative of cotangent function:   \dfrac{d}{dx}(\cot x)=-\csc^2 x
  • Derivative of secant function:   \dfrac{d}{dx}(\sec x)=\tan x\sec x
  • Derivative of cosecant function:   \dfrac{d}{dx}(\csc x)=-\cot x\csc x

 

Videos and Practice Problems of Selected Topics

  1. \rhd Derivatives of \sin(x) and \cos(x). (3:40)
  2. \rhd Worked Examples: derivatives of \sin(x) and \cos(x). (5:13) Find the derivative of g(x)=7\sin(x)-3\cos(x)-\left(\dfrac{\pi}{\sqrt[3]{x}}\right)^2.
  3. * Practice: Derivatives of \sin(x) and \cos(x). (4 problems)
  4. \rhd Derivatives of \tan(x) and \cot(x) (4:37) Use the quotient rule to derive formulas for the derivative of \tan(x) and \cot(x).
  5. \rhd Derivatives of \sec(x) and \csc(x) (4:27) Use the quotient rule to derive formulas for the derivative of \sec(x) and \csc(x).
  6. \rhd Product rule (8:03) Find the derivative of h(x) = (x^2)(x^3+4) (first 3:20 minutes) and y= (\sin x)(\cos x) (x^2+1).
  7. \rhd Quotient rule (7:37) Find the derivative of y=\dfrac{x^2+1}{x^5+x} (first 3:34 minues) and y=\dfrac{\tan x}{x^{3/2}+5x}.