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Austin Riley
Austin Riley asked in Science & MathematicsMathematics · 3 years ago

HELP ASAP PRE-CALC QUESTION cos(x)tan(x)+3√cos(x)=0?

(1 pt) cos(x)tan(x)+3√cos(x)=0

Find all angles in radians that satisfy the equation. For each solution enter first the angle solution in [0,π) or [0,2π) (depending on the trigonometric function) then the period. When 2 or more solutions are available enter them in increasing order of the angles. (e.g. x=π/2+2kπ or x=3π/2+kπ etc.)

Note: You are not allowed to use decimals in your answer. Use pi for π.

can you show the work on how this done??!!

Thank you so much!!

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  • DWRead
    Lv 7
    3 years ago

    You copied the equation incorrectly. The last term is √3cos(x), not 3√cos(x).

    cos(x)tan(x) + √3cos(x) = 0

    sin(x) + √3cos(x) = 0

    sin(x) = -√3cos(x)

    sin²(x) = 3cos²(x)

    1-cos²(x) = 3cos²(x)

    cos²(x) = ¼

    cos(x) = ±½

    x = π/3 + πk, 4π/3 + πk

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