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Linear Trigonometric Equations quiz

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  • What does it mean for a trigonometric equation to have multiple solutions?
    It means there are several angles that satisfy the equation, often due to the periodic nature of trig functions.
  • How do you find all solutions to a trig equation like sin(θ) = 1/2?
    First, find all solutions on the unit circle, then add 2πn (where n is an integer) to each solution to account for all rotations.
  • What are the solutions to sin(θ) = 1/2 in the interval 0 to 2π?
    The solutions are θ = π/6 and θ = 5π/6.
  • How do you express all solutions to sin(θ) = 1/2?
    All solutions are θ = π/6 + 2πn and θ = 5π/6 + 2πn, where n is any integer.
  • What is the only solution to cos(x) = -1 on the unit circle?
    The only solution is x = π.
  • How do you write all solutions to cos(x) = -1?
    All solutions are x = π + 2πn, where n is any integer.
  • What is the first step in solving a linear trigonometric equation?
    The first step is to isolate the trigonometric function using algebraic operations.
  • How do you treat the trig function when solving a linear trig equation?
    Treat the trig function as if it were a variable and use algebra to isolate it.
  • What are the solutions to 4sin(θ) - 3 = 1?
    First, isolate sin(θ) to get sin(θ) = 1, then θ = π/2 within 0 to 2π.
  • How do you solve -2cos(θ) + √3 = 0 for θ in [0, 2π]?
    Isolate cos(θ) to get cos(θ) = √3/2, then θ = π/6 and θ = 11π/6.
  • What do you do if the domain is restricted to 0 to 2π?
    Only include solutions within that interval and do not add 2πn.
  • Why do you add 2πn to solutions of trig equations?
    Because trig functions are periodic, adding 2πn accounts for all coterminal angles.
  • What is the general process for solving a linear trig equation?
    Isolate the trig function, solve for the angle using the unit circle, and add 2πn if the domain is unrestricted.
  • If cos(θ) = √3/2, what are the solutions in [0, 2π]?
    The solutions are θ = π/6 and θ = 11π/6.
  • What should you check after finding solutions to a trig equation?
    Check if the domain is restricted and only include solutions within the specified interval.