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Math Help - Solving trig equations

  1. #1
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    Solving trig equations

    Hi
    I need help on solving some of the following equations:
    1) Solve cos^2(x)-cos(x)sin(x) for x = [0,2\pi].

    2)Solve sec(x)=2.5 in the interval [-\pi,\pi], giving the answers correct to two decimal places.


    P.S
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  2. #2
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    Quote Originally Posted by Paymemoney View Post
    Hi
    I need help on solving some of the following equations:
    1) Solve cos^2(x)-cos(x)sin(x) for x = [0,2\pi].

    2)Solve sec(x)=2.5 in the interval [-\pi,\pi], giving the answers correct to two decimal places.


    P.S
    1. What is this expression equal to? If it's equal to 0 then factor

    cos(x)(cos(x)-sin(x)) = 0

    cos(x)=0 or cos(x) = sin(x)


    2.Take the reciprocal of both sides

    cos(x) = \frac{2}{5}
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  3. #3
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    yeh the first question is equal to 0
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  4. #4
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    in question 2 I'm not sure if i have done it correct:
    sec(x)=\frac{1}{cos(x)}
    so \frac{1}{\frac{2}{5}}=2.5*\frac{2}{5}
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  5. #5
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    Quote Originally Posted by e^(i*pi) View Post
    1. What is this expression equal to? If it's equal to 0 then factor

    cos(x)(cos(x)-sin(x)) = 0

    cos(x)=0 or cos(x) = sin(x)
    i get two solutions for when cos(x)=0, which are \frac{\pi}{2} & \frac{3\pi}{2}.
    However how do you get the solutions for cos(x)=sin(x)
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  6. #6
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    Quote Originally Posted by Paymemoney View Post
    i get two solutions for when cos(x)=0, which are \frac{\pi}{2} & \frac{3\pi}{2}.
    However how do you get the solutions for cos(x)=sin(x)
    Divide both sides by \cos{x}.


    So \tan{x} = 1.
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