Question

Find all real numbers on the interval [0.2 t) that satisfy the equation. Use radian measure.

Answer 1

Answer:

  x ∈ {2π/3, π, 4π/3} ≈ {2.09440, 3.14159, 4.18879}

Step-by-step explanation:

The equation can be put into standard form by adding 1:

  2cos²(x) +3cos(x) +1 = 0

  (2cos(x) +1)(cos(x) +1) = 0

Values of cos(x) that make this true* are ...

  cos(x) = -1/2 . . . . . . . . . true for x=2π/3, x=4π/3

  cos(x) = -1 . . . . . . . . . . . true for x=π

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A graphing calculator can be helpful here, too.

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* from your knowledge of the short table of trig functions and their signs in different quadrants