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? asked in Science & MathematicsMathematics · 2 years ago

Trig Help? TIA?

Solve the equation for x in [0,2pi). Round to nearest thousandth

5tan^2x-1=0

There are four answers

I am confused as to where to go. I have tanx=(square root 5)/5

Arctan(square root 5)/5

-Arctan(square root 5)/5

2 Answers

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  • Some Body
    Lv 7
    2 years ago
    Favorite Answer

    You're almost there.

    x = ±arctan(√5 / 5) + kπ

    x = ±0.421 + kπ

    Between 0 and 2π, the 4 values of x are:

    x = -0.421 + π = 2.721

    x = -0.421 + 2π = 5.862

    x = 0.421

    x = 0.421 + π = 3.562

  • Pinkgreen
    Lv 7
    2 years ago

    5tan^2(x)-1=0, where x is in [0, 2pi]=>

    tan(x)=+/-sqr(5)/5

    tan(x)=sqr(5)/5

    =>x=0.42, 3.56 radians

    tan(x)=-sqr(5)/5

    =>x=2.72, 5.86 radians

    Thus, the solutions are

    x=0.42, 2.72, 3.56 & 5.86

    radians approximately.

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