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Derivatives of Trig Functions definitions

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  • Sine Function
    A periodic curve whose derivative at any point equals the value of the cosine function at that point.
  • Cosine Function
    A periodic curve whose derivative at any point equals the negative value of the sine function at that point.
  • Tangent Function
    A trigonometric ratio expressible as sine divided by cosine, with a derivative equal to secant squared.
  • Secant Function
    A reciprocal trigonometric function whose derivative is the product of itself and the tangent function.
  • Cosecant Function
    A reciprocal trigonometric function whose derivative is the negative product of itself and the cotangent function.
  • Cotangent Function
    A trigonometric ratio expressible as cosine divided by sine, with a derivative equal to negative cosecant squared.
  • Product Rule
    A differentiation technique for products of functions, using the formula: left d right plus right d left.
  • Quotient Rule
    A differentiation technique for quotients, using the formula: low d high minus high d low, over the square of the denominator.
  • Higher Order Derivative
    A repeated differentiation process where every fourth derivative of sine or cosine returns to the original function.
  • Sum Rule
    A differentiation property allowing the derivative of a sum to be the sum of the derivatives.
  • Cofunction
    A trigonometric function whose derivative always carries a negative sign, such as cosine, cotangent, and cosecant.
  • Tangent Line
    A straight line that touches a curve at a single point, with its slope given by the derivative at that point.
  • Slope
    A measure of steepness of a curve at a point, numerically equal to the value of the derivative there.
  • Trig Identity
    An equation involving trigonometric functions, such as sine squared plus cosine squared equals one, often used in simplification.