Trigonometry Functions and Derivatives
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Questions and Answers

What is the relationship between sine and cosine in terms of tangent?

  • Sine is the reciprocal of cosine.
  • Cosine is the derivative of sine.
  • Sine over cosine equals tangent. (correct)
  • Cosine is greater than sine.

    • Which statement correctly describes the derivative of secant?

  • The derivative of sec(x) is -sec(x)tan(x).
  • The derivative of sec(x) is sec²(x).
  • The derivative of sec(x) is sec(x)tan(x). (correct)
  • The derivative of sec(x) is sec(x)cot(x).

    • What is the correct derivative for cosecant?

  • The derivative of csc(x) is csc²(x).
  • The derivative of csc(x) is sec(x)tan(x).
  • The derivative of csc(x) is -csc²(x).
  • The derivative of csc(x) is -csc(x)cot(x). (correct)

    • Which pair of trigonometric functions are considered 'best friends' due to their derivative relationships?

    <p>Tangent and secant.</p> Signup and view all the answers

    How is the derivative of cosine characterized?

    <p>It is -sin(x).</p> Signup and view all the answers

    Study Notes

    Organizing Trig Functions

    • Organize trig functions in this order: sine, cosine, tangent, cosecant, secant, cotangent.
    • This order helps remember relationships:
      • Sine over cosine equals tangent.
      • Cosecant is the reciprocal of sine (1/sine).
      • Secant is the reciprocal of cosine (1/cosine).
      • Cotangent is the reciprocal of tangent (1/tangent).

    Remembering Trig Function Derivatives

    • Best Friends: Memorize pairs of trig functions whose derivatives are related.
      • Sine and cosine are best friends.
      • Tangent and secant are best friends.
      • Cosecant and cotangent are best friends.

    Sine and Cosine Derivatives

    • Sine's best friend is cosine. The derivative of sin(x) is cos(x).
    • Cosine's best friend is sine. The derivative of cos(x) is -sin(x) (negative, due to the "co" in cosine).

    Tangent and Secant Derivatives

    • Tangent's best friend is secant. The derivative of tan(x) is sec²(x).
    • Secant's best friend is tangent. The derivative of sec(x) is sec(x)tan(x).

    Cosecant and Cotangent Derivatives

    • Cosecant's best friend is cotangent. The derivative of csc(x) is -csc(x)cot(x) (negative, due to the "co" in cosecant).
    • Cotangent's best friend is cosecant. The derivative of cot(x) is -csc²(x) (negative, due to the "co" in cotangent).

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    Description

    This quiz covers the organization of trigonometric functions and their derivatives. You'll learn about the relationships between sine, cosine, tangent, and their respective reciprocals. Memorization strategies will help you remember the derivatives of these essential functions.

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