SOLUTION: Determine all the values where -3sinx=√3 cosx for 0 degrees less than an equal to x less than an equal to 360 degrees. thank you so much

Question 1194997: Determine all the values where -3sinx=√3 cosx for 0 degrees less than an equal to x less than an equal to 360 degrees.
thank you so much
Answer by ikleyn(52811)   (Show Source): You can put this solution on YOUR website!
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Determine all the values where -3*sinx = √3*cosx for 0 <= x < 360 degrees.
~~~~~~~~~~~~~~~~~~~~~~

            I specially re-wrote your formulation in order for
            you learn on how to do it in a right way.

Your original equation is

    -3*sin(x) = .


Divide both sides by -3*cos(x).  You will get an EQUIVALENT equation

    tan(x) = .


In the given interval  0 <= x < 360  it has presicely two solutions

    x = 150 degrees  and  x = 330 degrees.    ANSWER

Solved.

--------------

A person who loves accurate mathematical solutions, may ask me why I divided the original
equation by cos(x) without taking care that cos(x) can be equal to 0 (zero).

        It is right question.

The   answer   is :   it is because if cos(x) = 0, then due to the given equation, sin(x) = 0;
but sin(x) and cos(x) may not be equal to zero simultaneously.

        So, the case cos(x) = 0 is EXCLUDED by the given equation ( ! )

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