Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

please help? Find ALL exact radian solutions to the equation: sinx + 2sinxcosx = 0?

Update:

ALL solutions should involve K

1 Answer

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  • Alan
    Lv 7
    1 month ago
    Favorite Answer

    sinx + 2sinxcosx =0 

    sin(x) *(1   + 2*cos(x) ) ) = 0 

    so either 

    sin(x) = 0 

    x = arcsin(0)  + 2pi*k    

    x =  0 or pi + 2pi*k 

    x = 0  +pi*k  (where k is an integer )

    or 

    1 + 2*cos(x) = 0 

    2*cos(x) = -1 

    cos(x) = -1/2   

    x = arcos(-1/2) + 2pi*k 

    x =  (2/3) pi  +2pi*k or   (4/3)pi  + 2pi*k 

    so all answer are 

    0 + pi*k  ,   (2/3)pi + 2pi*k  , (4/3)pi+ 2pi*k 

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