trig plz help

posted by brittney

Solve, finding all solutions in the interval [0, 2π). tan(3x) = -1

  1. Reiny

    tan (3x) = -1
    I know that 3x must be in quadrants II or IV
    and I know that tan 45° = +1 or tan π/4 = 1
    so 3x = π - π/4 OR 3x = 2π - π/4
    3x = 3π/4 or 3x = 7π/4
    x = π/4 or x = 7π/12

    now the period of tan 3x is π/3
    so adding multiples of π/3 to any answer will yield a new answer.

    x = π/4
    x = π/4 + π/3 = 7π/12 , we already have that one
    x = 7π/12 + π/3 = 11π/12
    x = 11π/12 + π/3 = 5π/4
    x = 5π/4 + π/3 = 19π/12
    x = 19π/12 + π/3 = 23π/12
    The next one will be > 2π

    So we have the above 6 solutions in the required domain.

    btw, in degrees,
    x = 45°, 105°, 165°, 225°, 285, and 345°

    check two of them:
    tan(3(105)) = -1
    tan(3(345) = -1

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