Derivatives of remaining trigonometric functions:

• What is the tangent function defined as in terms of sine and cosine?

  $\tan(x) =$$\frac{\sin(x)}{\cos(x)}$
• What is the period of the tangent function?

  $\pi$
• What is the formula for the derivative of sec x?

  $\frac{d}{dx} \sec x =$$\sec x \tan x$
• The derivative of cosecant is -csc x cot x.

  True
• The derivative of the cotangent function is -csc^2 x.


  True
• How is the derivative of sec x calculated using the quotient rule?

  \frac{d}{dx} \sec x = \sec x \tan x</latex>
• At what values of x is the tangent function undefined?

  Multiples of π/2
• What is the derivative of the secant function?

  sec x tan x
• The derivative of cot x is -csc^2 x.


  True
• The derivative of sin(3x) is 9 cos(3x).

  True
• The derivative of secant is found using the quotient rule.
• The cosecant function is defined as $\csc x =$$\frac{1}{\sin x}$.
• The cotangent function is defined as $\cot x =$$\frac{\cos x}{\sin x}$.
• Match the basic trigonometric function with its key properties:

  1️⃣ Sine

  2️⃣ Period: 2π, Amplitude: 1
• What is the period of the sine function?

  2π
• The secant function is defined as sec x = 1 / cos x
• What is the definition of the cosecant function?

  csc x = 1 / sin x
• The derivative of the cotangent function is -csc^2 x
• The sine function has a period of 2π and an amplitude of 1.


  True
• The derivative of secant is sec x tan x.


  True
• What is the derivative of csc x?

  $\frac{d}{dx} \csc x =$$- \csc x \cot x$
• What is the derivative of cot x?

  $\frac{d}{dx} \cot x =$$- \csc^{2} x$
• The tangent function is undefined at multiples of $\frac{\pi}{2}$.
• What is the amplitude of the cosine function?

  1
• The derivative of sec x is sec x tan x.


  True
• What is the derivative of csc x?

  -csc x cot x
• What does the chain rule state for derivatives?

  d/dx y = d/dg(x) f(g(x)) * d/dx g(x)