Solving Simultaneous Equations with Trigonometric Functions
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Questions and Answers

In Illustration 4, what is the most general value of θ that satisfies both equations?

  • θ = 2nπ + 7π/6 (correct)
  • θ = nπ + π/6
  • θ = 2nπ + π/6
  • θ = nπ + 7π/6

    • In Illustration 5, what is the smallest positive value of A + B?

  • π/6
  • π/3
  • π/2 (correct)
  • π/4

    • In Illustration 5, what is the smallest positive value of A - B?

  • π/4
  • π/6 (correct)
  • π/3
  • π/2

    • In Illustration 4, which of the following is NOT a value of θ that satisfies the equation sin θ = -1/2?

    <p>θ = π/6</p> Signup and view all the answers

    In Illustration 5, which of the following is NOT a general value of A - B?

    <p>A - B = 2nπ + π/2</p> Signup and view all the answers

    In Illustration 5, which of the following is NOT a general value of A + B?

    <p>A + B = nπ + π/4</p> Signup and view all the answers

    What is the smallest positive angle whose sine is 1/2?

    <p>π/6</p> Signup and view all the answers

    What is the general solution for the equation cos θ = -1/2?

    <p>θ = nπ + (-1)^n * π/3</p> Signup and view all the answers

    What is the general solution for the equation sin θ = 1?

    <p>θ = (4n + 1)π/2</p> Signup and view all the answers

    What is the general solution for the equation sin θ = sin α?

    <p>θ = 2nπ + α</p> Signup and view all the answers

    What is the general solution for the equation cos θ = cos α?

    <p>θ = nπ + α</p> Signup and view all the answers

    What is the general solution for the equation tan θ = tan α?

    <p>θ = nπ + α</p> Signup and view all the answers

    What is the general solution for the equation sin  = sin ?

    <p>    = n + (– 1)n  ; nI ;    ,   2 2</p> Signup and view all the answers

    What is the general solution for the equation cos  = cos ?

    <p> = 2n ± ; nI;  [0, ]</p> Signup and view all the answers

    What is the general solution for the equation tan  = tan ?

    <p> = n + ; nI;    ,    2 2</p> Signup and view all the answers

    What is the smallest positive value of  that satisfies cos  = cos ?

    <p>/4</p> Signup and view all the answers

    What is the smallest positive value of  that satisfies tan  = tan , given that  is in the first quadrant?

    <p>/4</p> Signup and view all the answers

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